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Charging the Conformal Window
by Orlando, Domenico on 20 March 2020 at 2:41
arXiv:2003.08396by: Orlando, DomenicoAbstract: We investigate the properties of nearconformal dynamics in a sector of large charge when approaching the lower boundary of the conformal window from the chirally broken phase. To elucidate our approach we use the timehonored example of the phenomenologically relevant SU(2) color theory featuring $N_f$ Dirac fermions transforming in the fundamental representation of the gauge group. In the chirally broken phase we employ the effective pion Lagrangian featuring also a pseudodilaton to capture a possible smooth conformaltononconformal phase transition. We charge the baryon symmetry of the Lagrangian and study its impact on the ground state and spectrum of the theory as well as the wouldbe conformal dimensions of the lowest largecharge operator. We moreover study the effects of and dependence on the fermion mass term. […]

Supersymmetric Wilson Loops via Integral Forms
by Cremonini, C.A. on 5 March 2020 at 3:18
arXiv:2003.01729by: Cremonini, C.A. (INFN, Milan) et al.Abstract: We study supersymmetric Wilson loops from a geometrical perspective. To this end, we propose a new formulation of these operators in terms of an integral form associated to the immersion of the loop into a supermanifold. This approach provides a unifying description of Wilson loops preserving different sets of supercharges, and clarifies the flow between them. Moreover, it allows to exploit the powerful techniques of superdifferential calculus for investigating their symmetries. As remarkable examples, we discuss supersymmetry and kappasymmetry invariance. […]

On the Origin of Divergences in TimeDependent Orbifolds
by Arduino, Andrea on 27 February 2020 at 3:13
arXiv:2002.11306by: Arduino, Andrea (U. Turin (main)) et al.Abstract: We consider timedependent orbifolds in String Theory and we show that divergences are not associated with a gravitational backreaction since they appear in the open string sector too. They are related to the non existence of the underlying effective field theory as in several cases fourth and higher order contact terms do not exist. Since contact terms may arise from the exchange of string massive states, we investigate and show that some three points amplitudes with one massive state in the open string sector are divergent on the timedependent orbifolds. To check that divergences are associated with the existence of a discrete zero eigenvalue of the Laplacian of the subspace with vanishing volume, we construct the Generalized Null Boost Orbifold where this phenomenon can be turned on and off. […]

ChernSimons Supergravity on Supergroup Manifolds
by Castellani, L. on 24 February 2020 at 2:47
arXiv:2002.09400by: Castellani, L. (Piemonte Orientale U., Alessandria) et al.Abstract: We construct N=1 d=3 AdS supergravity within the group manifold approach and compare it with AchucarroTownsend ChernSimons formulation of the same theory. We clarify the relation between the offshell super gauge transformations of the ChernSimons theory and the offshell worldvolume supersymmetry transformations of the group manifold action. We formulate the AchucarroTownsend model in a double supersymmetric action where the ChernSimons theory with a supergroup gauge symmetry is constructed on a supergroup manifold. This framework is useful to establish a correspondence of degrees of freedom and auxiliary fields between the two descriptions of d=3 supergravity. […]

Heterotic − type I dual pairs, rigid branes and broken SUSY
by Angelantonj, Carlo on 30 December 2019 at 2:50
arXiv:1912.12062CPHTRR105.122019Nucl.Phys. B954 (2020) 114976by: Angelantonj, Carlo (INFN, Turin) et al.Abstract: The moduli space of toroidal type I vacua, which are consistent at the nonperturbative level, is composed of independent branches characterized by the number (0, 16 or 32) of rigid branes sitting on top of orientifold planes. This structure persists also when supersymmetry is spontaneously broken à la Scherk–Schwarz. We show that all the components of the moduli space in dimension D≥5 indeed admit heterotic dual components, by explicitly constructing heterotictype I dual pairs with the rank of the gauge group reduced by 0, 8 or 16 units. In the presence of spontaneous breaking of supersymmetry, the dual pairs we consider are also free of tachyonic instabilities at the oneloop level, provided the scale of supersymmetry breaking is lower than the string scale. […]

Super ChernSimons Theory: BVformalism and $A_\infty$algebras
by Cremonini, C.A. on 24 December 2019 at 3:15
arXiv:1912.10807ARC1925by: Cremonini, C.A. (Milan U.) et al.Abstract: This is a companion paper of a long work appeared in [1] discussing the superChernSimons theory on supermanifolds. Here, it is emphasized that the BV formalism is naturally formulated using integral forms for any supersymmetric and supergravity models and we show how to deal with $A_\infty$algebras emerging from supermanifold structures. […]

On the $T\bar T$ deformation of the compactified boson and its interpretation in Lattice Gauge Theory
by Beratto, Emanuele on 19 December 2019 at 2:55
arXiv:1912.08654by: Beratto, Emanuele (Milan Bicocca U.) et al.Abstract: We study the effective string description of spacelike Polyakov loop correlators at finite temperature with the goal of describing the behaviour of the spacelike string tension in the vicinity of the deconfinement transition. To this end we construct the partition function of the NambuGoto effective string theory in presence of a compact transverse direction of length $L$ equal to the inverse temperature. We then show that, under particular conditions, our result can be interpreted as the partition function of the $T\bar T$ deformation of the 2d quantum field theory describing a compactified bosonic field and that this mapping allows a deeper insight on the behaviour of the spacelike observables of the theory. In particular we show, by imposing that the spectrum of the model obeys the inviscid Burgers equation, that the $T\bar T$ deformations follow well defined trajectories in the parameter space $(\sigma,L)$ of the model, where $\sigma$ is the string tension, which are characterized by a constant value of the dimensionless compactification radius $\rho=L\sqrt{\sigma/2\pi}$. We discuss the potential usefulness of these results for studying the spacelike string tension of the underlying Lattice Gauge Theory and its behaviour across the deconfinement transition. […]

2D Fermion on the Strip with Boundary Defects as a CFT with Excited Spin Fields
by Finotello, Riccardo on 18 December 2019 at 3:25
arXiv:1912.07617by: Finotello, Riccardo (Turin U.) et al.Abstract: We consider a twodimensional fermion on the strip in the presence of an arbitrary number of zerodimensional boundary changing defects. We show that the theory is still conformal with time dependent stressenergy tensor and that the allowed defects can be understood as excited spin fields. Finally we compute correlation functions involving these excited spin fields without using bosonization. […]

Localization of effective actions in Heterotic String Field Theory
by Erbin, Harold on 12 December 2019 at 3:49
arXiv:1912.05463JHEP 2002 (2020) 059by: Erbin, Harold (Turin U.) et al.Abstract: We consider the algebraic couplings in the tree level effective action of the heterotic string. We show how these couplings can be computed from closed string field theory. When the light fields we are interested in are charged under an underlying $ \mathcal{N} $ = 2 Rcharge in the leftmoving sector, their quartic effective potential localizes at the boundary of the worldsheet moduli space, in complete analogy to the previously studied open string case. In particular we are able to compute the quartic closed string field theory potential without resorting to any explicit expression for the 3 and the 4strings vertices but only using the L$_{∞}$ relations between them. As a non trivial example we show how the heterotic YangMills quartic potential arises in this way. […]

YangBaxter deformations and generalized supergravity  A short summary
by Orlando, Domenico on 6 December 2019 at 3:18
arXiv:1912.02553by: Orlando, Domenico (INFN, Turin) et al.Abstract: Integrable deformations of type IIB superstring theory on $\mathrm{AdS}_5\times S^5$ have played an important role over the last years. The YangBaxter deformation is a systematic way of generating such integrable deformations. Since its introduction, this topic has seen important conceptual progress and has among others led to the intriguing discovery generalized supergravity, a new lowenergy effective theory. This review endeavors to not only introduce the historical development of the YangBaxter deformation, but also its relation to generalized supergravity, nongeometric backgrounds, nonabelian Tduality and preserved Killing spinors. We supplement the general treatment with a wealth of explicit examples. […]

On Positive Geometries of Quartic Interactions II : Stokes polytopes, Lower Forms on Associahedra and Worldsheet Forms
by Aneesh, P.B. on 15 November 2019 at 3:04
arXiv:1911.06008by: Aneesh, P.B. (Chennai Math. Inst.) et al.Abstract: In [1], two of the present authors along with P. Raman attempted to extend the Amplituhedron program for scalar field theories [2] to quartic scalar interactions. In this paper we develop various aspects of this proposal. Using recent seminal results in Representation theory [3,4], we show that projectivity of scattering forms and existence of kinematic space associahedron completely capture planar amplitudes of quartic interaction. We generalise the results of [1] and show that for any $n$particle amplitude, the positive geometry associated to the projective scattering form is a convex realisation of Stokes polytope which can be naturally embedded inside one of the ABHY associahedra defined in [2,5]. For a special class of Stokes polytopes with hypercubic topology, we show that they have a canonical convex realisation in kinematic space as boundaries of kinematic space associahedra. We then use these kinematic space geometric constructions to write worldsheet forms for $\phi^{4}$ theory which are forms of lower rank on the CHY moduli space. We argue that just as in the case of biadjoint $\phi^3$ scalar amplitudes, scattering equations can be used as diffeomorphisms between certain $\frac{n4}{2}$ forms on the worldsheet and $\frac{n4}{2}$ forms on ABHY associahedron that generate quartic amplitudes. […]

On Curvature and Torsion in Courant Algebroids
by Aschieri, Paolo on 25 October 2019 at 3:06
arXiv:1910.11273by: Aschieri, Paolo (Piemonte Orientale U., Alessandria) et al.Abstract: We study the graded geometric point of view of curvature and torsion of Qmanifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly restrict to Dirac structures. Depending on an auxiliary affine connection K, we introduce the Kcurvature and Ktorsion of a Courant algebroid connection. These are conventional tensors on the body. Finally, we compute their Ricci and scalar curvature. […]

Emitted Radiation and Geometry
by Bianchi, Lorenzo on 16 October 2019 at 7:04
arXiv:1910.06332JHEP 2001 (2020) 075by: Bianchi, Lorenzo (Queen Mary, U. of London) et al.Abstract: In conformal $ \mathcal{N} $ = 2 Super YangMills theory, the energy emitted by an accelerated heavy particle is computed by the onepoint function of the stress tensor operator in the presence of a Wilson line. In this paper, we consider the theory on the ellipsoid and we prove a conjectured relation between the stress tensor onepoint function and the first order expansion of the Wilson loop expectation value in the squashing parameter. To do this, we analyze the behavior of the Wilson loop for a small deformation of the background geometry and, at first order in the deformation, we fix the kinematics using defect CFT constraints. In the final part of the paper, we analyze the consequences of our results for the weak coupling perturbative expansion. In particular, comparing the weakly coupled matrix model with the ordinary Feynman diagram expansion, we find a natural transcendentality driven organization for the latter. […]

$\mathcal{N}$extended $D = 4$ supergravity, unconventional SUSY and graphene
by Andrianopoli, L. on 9 October 2019 at 3:08
arXiv:1910.03508JHEP 2001 (2020) 084by: Andrianopoli, L. (Turin Polytechnic) et al.Abstract: We derive a 2+1 dimensional model with unconventional supersymmetry at the boundary of an AdS$_{4} \mathcal{N} $ extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a topdown approach, the electronic properties of graphenelike 2D materials at the two Dirac points, K and K′. The two valleys correspond to the two independent sectors of the OSp(p2) × OSp(q2) boundary model in the p = q case, which are related by a parity transformation. The Semenoff and Haldanetype masses entering the corresponding Dirac equations are identified with the torsion parameters of the substrate in the model. […]

The String Geometry Behind Topological Amplitudes
by Angelantonj, Carlo on 9 October 2019 at 3:07
arXiv:1910.03347JHEP 2001 (2020) 005by: Angelantonj, Carlo (INFN, Turin) et al.Abstract: It is shown that the generating function of $ \mathcal{N} $ = 2 topological strings, in the heterotic weak coupling limit, is identified with the partition function of a sixdimensional Melvin background. This background, which corresponds to an exact CFT, realises in string theory the sixdimensional Ωbackground of Nekrasov, in the case of opposite deformation parameters ϵ$_{l}$ = −ϵ$_{2}$, thus providing the known perturbative part of the Nekrasov partition function in the field theory limit. The analysis is performed on both heterotic and type I strings and for the cases of ordinary $ \mathcal{N} $ = 2 and $ \mathcal{N} $ = 2* theories. […]

String field theory solution for any open string background. Part II
by Erler, Theodore on 27 September 2019 at 12:34
arXiv:1909.11675JHEP 2001 (2020) 021by: Erler, Theodore (ASCR, Prague) et al.Abstract: Generalizing previous work, we give a new analytic solution in Witten’s open bosonic string field theory which can describe any open string background. The central idea is to use Riemann surface degenerations as a mechanism for taming OPE singularities. This requires leaving the familiar subalgebra of wedge states with insertions, but the payoff is that the solution makes no assumptions about the reference and target Dbrane systems, and is therefore truly general. For example, unlike in previous work, the solution can describe time dependent backgrounds and multiple copies of the reference Dbrane within the universal sector. The construction also resolves some subtle issues resulting from associativity anomalies, giving a more complete understanding of the relation between the degrees of freedom of different Dbrane systems, and a nonperturbative proof of background independence in classical open bosonic string field theory. […]

NearConformal Dynamics at Large Charge
by Orlando, Domenico on 20 September 2019 at 2:47
arXiv:1909.08642CP3Origins201936 DNRF90Phys.Rev. D101 (2020) 065018by: Orlando, Domenico (INFN, Turin) et al.Abstract: We investigate fourdimensional nearconformal dynamics by means of the largecharge limit. We first introduce and justify the formalism in which nearconformal invariance is insured by adding a dilaton and then determine the largecharge spectrum of the theory. The dilaton can also be viewed as the radial mode of the EFT. We calculate the twopoint functions of charged operators. We discover that the mass of the dilaton, parametrising the nearbreaking of conformal invariance, induces a novel term that is logarithmic in the charge. One can therefore employ the largecharge limit to explore nearconformal dynamics and determine dilatonrelated properties. […]

Large charge at large N
by AlvarezGaume, Luis on 9 September 2019 at 4:19
arXiv:1909.02571JHEP 1912 (2019) 142by: AlvarezGaume, Luis (Stony Brook U., New York, SCGP) et al.Abstract: We apply the largecharge expansion to O(N) vector models starting from first principles, focusing on the WilsonFisher point in three dimensions. We compute conformal dimensions at zero and finite temperature at fixed charge Q, concentrating on the regime 1 « N « Q. Our approach places the earlier effective field theory treatment on firm ground and extends its predictions. […]

Modular Bootstrap, Elliptic Points, and Quantum Gravity
by Gliozzi, Ferdinando on 2 August 2019 at 3:01
arXiv:1908.00029Phys.Rev.Res. 2 (2020) 013327Phys.Rev.Research. 2 (2020) 013327by: Gliozzi, Ferdinando (INFN, Turin)Abstract: The modular bootstrap program for twodimensional conformal field theories could be seen as a systematic exploration of the physical consequences of consistency conditions at the elliptic points and at the cusp of their torus partition function. The study at τ=i, the elliptic point stabilized by the modular inversion S, was initiated by Hellerman [S. Hellerman, J. High Energy Phys. 08 (2011) 130JHEPFG1029847910.1007/JHEP08(2011)130], who found a general upper bound for the most relevant scaling dimension Δ. Likewise, analyticity at τ=i∞, the cusp stabilized by the modular translation T, yields an upper bound on the twist gap. Here we study consistency conditions at τ=exp(2iπ/3), the elliptic point stabilized by ST. We find a much stronger upper bound in the largec limit, namely, &Delta […]

Pictures from Super ChernSimons Theory
by Cremonini, C.A. on 17 July 2019 at 11:31
arXiv:1907.07152ARC1908JHEP 2003 (2020) 043by: Cremonini, C.A. (Milan U.) et al.Abstract: We study superChernSimons theory on a generic supermanifold. After a selfcontained review of integration on supermanifolds, the complexes of forms (superforms, pseudoforms and integral forms) and the extended Cartan calculus are discussed. We then introduce Picture Changing Operators. We provide several examples of computation of PCO's acting on different type of forms. We illustrate also the action of the $\eta$ operator, crucial ingredient to define the interactions of super ChernSimons theory. Then, we discuss the action for super ChernSimons theory on any supermanifold, first in the factorized form (3form $\times$ PCO) and then, we consider the most general expression. The latter is written in term of psuedoforms containing an infinite number of components. We show that the free equations of motion reduce to the usual ChernSimons equations yielding the proof of the equivalence between the formulations at different pictures of the same theory. Finally, we discuss the interaction terms. They require a suitable definition in order to take into account the picture number. That implies the construction of a 2product which is not associative that inherits an $A_\infty$ algebra structure. That shares several similarities with a recent construction of a super string field theory action by Erler, Konopka and Sachs. […]

$O(d,d)$ transformations preserve classical integrability
by Orlando, Domenico on 10 July 2019 at 3:04
arXiv:1907.03759KUNS2767Nucl.Phys. B950 (2020) 114880by: Orlando, Domenico (Turin U.) et al.Abstract: In this note, we study the action of O(d,d) transformations on the integrable structure of twodimensional nonlinear sigma models via the doubled formalism. We construct the Lax pairs associated with the O(d,d) transformed model and find that they are in general nonlocal because they depend on the winding modes. We conclude that every O(d,d;R) deformation preserves integrability. As an application we compute the Lax pairs for continuous families of deformations, such as JJ¯ marginal deformations and TsT transformations of the threesphere with H flux. […]

The $\mathcal{N}_3=3\to \mathcal{N}_3=4$ enhancement of Super ChernSimons theories in $D=3$, Calabi HyperKähler metrics and M2branes on the $\mathcal{C}(\mathrm{N^{0,1,0}})$ conifold
by Fré, P. on 28 June 2019 at 8:09
arXiv:1906.11672ARC1907by: Fré, P. (Turin U.) et al.Abstract: Considering matter coupled supersymmetric ChernSimons theories in three dimensions we extend the GaiottoWitten mechanism of supersymmetry enhancement $\mathcal{N}_3=3\to \mathcal{N}_3=4$ from the case where the hypermultiplets span a flat HyperK\"ahler manifold to that where they live on a curved one. We derive the precise conditions of this enhancement in terms of generalized GaiottoWitten identities to be satisfied by the triholomorphic moment maps. An infinite class of HyperK\"ahler metrics compatible with the enhancement condition is provided by the Calabi metrics on $T^\star \mathbb{P}^{n}$. In this list we find, for $n=2$ the resolution of the metric cone on $\mathrm{N}^{0,1,0}$ which is the unique homogeneous Sasaki Einstein 7manifold leading to an $\mathcal{N}_4=3$ compactification of Mtheory. This leads to challenging perspectives for the discovery of new relations between the enhancement mechanism in $D=3$, the geometry of M2brane solutions and also for the dual description of super Chern Simons theories on curved HyperK\"ahler manifolds in terms of gauged fixed supergroup Chern Simons theories. The relevant supergroup is in this case $\mathrm{SU(3N)}$ where $\mathrm{SU(3)}$ is the flavor group and $\mathrm{U(N)}$ is the color group. […]

BPS wilson loops in generic conformal $ \mathcal{N} $ = 2 SU(N) SYM theories
by Billò, M. on 18 June 2019 at 3:05
arXiv:1906.07085JHEP 1908 (2019) 108by: Billò, M. (Turin U.) et al.Abstract: We consider the 1/2 BPS circular Wilson loop in a generic $ \mathcal{N} $ = 2 SU(N) SYM theory with conformal matter content. We study its vacuum expectation value, both at finite N and in the largeN limit, using the interacting matrix model provided by localization results. We single out some families of theories for which the Wilson loop vacuum expectation values approaches the $ \mathcal{N} $ = 4 result in the largeN limit, in agreement with the fact that they possess a simple holographic dual. At finite N and in the generic case, we explicitly compare the matrix model result with the fieldtheory perturbative expansion up to order g$^{8}$ for the terms proportional to the Riemann value ζ (5), finding perfect agreement. Organizing the Feynman diagrams as suggested by the structure of the matrix model turns out to be very convenient for this computation. […]

Modular properties of surface operators in $N=2$ SQCD
by Ballav, Sourav on 28 May 2019 at 3:04
arXiv:1905.10898JHEP 1907 (2019) 177by: Ballav, Sourav (HBNI, Mumbai) et al.Abstract: We study halfBPS surface operators in $ \mathcal{N} $ = 2 supersymmetric QCD in four dimensions with gauge group SU(2) and four fundamental flavours. We compute the twisted chiral superpotential that describes the effective theory on the surface operator using equivariant localization as well as the SeibergWitten data. We then use the constraints imposed by Sduality to resum the instanton contributions to the twisted superpotential into elliptic functions and (quasi) modular forms. The resummed results match what one would obtain from the description of surface operators as the insertion of a degenerate operator in a spherical conformal block in Liouville CFT. […]

Localization of effective actions in open superstring field theory: small Hilbert space
by Maccaferri, Carlo on 14 May 2019 at 8:55
arXiv:1905.04958JHEP 1906 (2019) 101by: Maccaferri, Carlo (Turin U.) et al.Abstract: We consider the algebraic effective couplings for open superstring massless modes in the framework of the $A_\infty$ theory in the small Hilbert space. Focusing on quartic algebraic couplings, we reduce the effective action of the $A_\infty$ theory to the Berkovits one where we have already shown that such couplings are fully computed from contributions at the boundary of moduli space, when the massless fields under consideration are appropriately charged under an ${\cal N}\!=\!2$ $R$symmetry. Here we offer a proof of localization which is in the small Hilbert space. We also discuss the flat directions of the obtained quartic potentials and give evidence for the existence of exactly marginal deformations in the $D3/D(1)$ system in the framework of string field theory. […]

A safe CFT at large charge
by Orlando, Domenico on 2 May 2019 at 2:46
arXiv:1905.00026JHEP 1908 (2019) 164by: Orlando, Domenico (INFN, Turin) et al.Abstract: We apply the largecharge limit to the first known example of a fourdimensional gaugeYukawa theory featuring an ultraviolet interacting fixed point in all couplings. We determine the energy of the ground state in presence of large fixed global charges and deduce the global symmetry breaking pattern. We show that the fermions decouple at low energy leaving behind a confining YangMills theory and a characteristic spectrum of type I (relativistic) and type II (nonrelativistic) Goldstone bosons. Armed with the knowledge acquired above we finally arrive at establishing the conformal dimensions of the theory as a triple expansion in the largecharge, the number of flavors and the controllably small inverse gauge coupling constant at the UV fixed point. Our results unveil a number of noteworthy properties of the lowenergy spectrum, vacuum energy and conformal properties of the theory. They also allow us to derive a new consistency condition for the relative sizes of the couplings at the fixed point. […]

The Quantum Theory of ChernSimons Supergravity
by Andrianopoli, L. on 12 March 2019 at 3:22
arXiv:1903.04431ARC1818JHEP 1906 (2019) 036by: Andrianopoli, L. (Turin Polytechnic) et al.Abstract: We consider AdS$_{3}$Nextended ChernSimons supergravity (à la AchucarroTownsend) and we study its gauge symmetries. We promote those gauge symmetries to a BRST symmetry and we perform its quantization by choosing suitable gaugefixings. The resulting quantum theories have different features which we discuss in the present work. In particular, we show that a special choice of the gaugefixing correctly reproduces the Ansatz by Alvarez, Valenzuela and Zanelli for the graphene fermion. […]

Conformal dimensions in the large charge sectors at the O(4) WilsonFisher fixed point
by Banerjee, Debasish on 27 February 2019 at 2:45
arXiv:1902.09542Phys.Rev.Lett. 123 (2019) 051603by: Banerjee, Debasish (Humboldt U., Berlin) et al.Abstract: We study the O(4) WilsonFisher fixed point in 2+1 dimensions in fixed largecharge sectors identified by products of two spinj representations (jL,jR). Using effective field theory we derive a formula for the conformal dimensions D(jL,jR) of the leading operator in terms of two constants, c3/2 and c1/2, when the sum jL+jR is much larger than the difference jLjR. We compute D(jL,jR) when jL=jR with Monte Carlo calculations in a discrete formulation of the O(4) lattice field theory, and show excellent agreement with the predicted formula and estimate c3/2=1.068(4) and c1/2=0.083(3). […]

Crepant resolutions of $\mathbb{C}^3/\mathbb{Z}_4$ and the generalized Kronheimer construction (in view of the gauge/gravity correspondence)
by Bruzzo, Ugo on 5 February 2019 at 3:15
arXiv:1902.01060J.Geom.Phys. 145 (2019) 103467by: Bruzzo, Ugo (INFN, Trieste) et al.Abstract: As a continuation of a general program started in two previous publications, in the present paper we study the K\"ahler quotient resolution of the orbifold $\mathbb{C}^3/\mathbb{Z}_4$, comparing with the results of a toric description of the same. In this way we determine the algebraic structure of the exceptional divisor, whose compact component is the second Hirzebruch surface $\mathbb F_2$. We determine the explicit K\"ahler geometry of the smooth resolved manifold $Y$, which is the total space of the canonical bundle of $\mathbb F_2$. We study in detail the chamber structure of the space of stability parameters (corresponding in gauge theory to the FayetIliopoulos parameters) that are involved in the construction of the desingularizations either by generalized Kronheimer quotient, or as algebrogeometric quotients. The walls of the chambers correspond to two degenerations; one is a partial desingularization of the quotient, which is the total space of the canonical bundle of the weighted projective space $\mathbb P[1,1,2]$, while the other is the product of the ALE space $A_1$ by a line, and is related to the full resolution in a subtler way. These geometrical results will be used to look for exact supergravity brane solutions and dual superconformal gauge theories. […]

Twopoint correlators in nonconformal $ \mathcal{N} $ = 2 gauge theories
by Billo, M. on 29 January 2019 at 5:41
arXiv:1901.09693ROM2F/2019/02JHEP 1905 (2019) 199by: Billo, M. (Turin U.) et al.Abstract: We study the twopoint correlation functions of chiral/antichiral operators in $ \mathcal{N} $ = 2 supersymmetric YangMills theories on $ \mathbb{R}^{4}$ with gauge group SU(N) and N$_{f}$ massless hypermultiplets in the fundamental representation. We compute them in perturbation theory, using dimensional regularization up to two loops, and show that fieldtheory observables built out of dimensionless ratios of twopoint renormalized correlators on $ \mathbb{R}^{4}$ are in perfect agreement with the same quantities computed using localization on the foursphere, even in the nonconformal case N$_{f}$ ≠ 2N. […]

Surface operators in $N=$ 2 SQCD and Seiberg Duality
by Ashok, Sujay K. on 29 January 2019 at 3:11
arXiv:1901.09630Eur.Phys.J. C79 (2019) 372by: Ashok, Sujay K. (HBNI, Mumbai) et al.Abstract: We study halfBPS surface operators in $\mathcal {N}=2$ supersymmetric asymptotically conformal gauge theories in four dimensions with SU(N) gauge group and 2N fundamental flavours using localization methods and coupled 2d/4d quiver gauge theories. We show that contours specified by a particular Jeffrey–Kirwan residue prescription in the localization analysis map to particular realizations of the surface operator as flavour defects. Seiberg duality of the 2d/4d quivers is mapped to contour deformations of the localization integral which in this case involves a residue at infinity. This is reflected as a modified Seiberg duality rule that shifts the Lagrangian of the purported dual theory by nonperturbative terms. The new rules, that depend on the 4d gauge coupling, lead to a match between the low energy effective twisted chiral superpotentials for any pair of dual 2d/4d quivers. […]

Taming boundary condition changing operator anomalies with the tachyon vacuum
by Erler, Theodore on 24 January 2019 at 3:49
arXiv:1901.08038JHEP 1906 (2019) 027by: Erler, Theodore (Prague, Inst. Phys.) et al.Abstract: Motivated by the appearance of associativity anomalies in the context of superstring field theory, we give a generalized solution built from boundary condition changing operators which can be associated to a generic tachyon vacuum in the KBc subalgebra of the Okawa form. We articulate sufficient conditions on the choice of tachyon vacuum to ensure that ambiguous products do not appear in the equations of motion. […]

$A_\infty$Algebra from Supermanifolds
by Catenacci, Roberto on 4 January 2019 at 4:11
arXiv:1901.00818ARC1814Annales Henri Poincare 20 (2019) 41634195by: Catenacci, Roberto (Piemonte Orientale U., Alessandria) et al.Abstract: Inspired by the analogy between different types of differential forms on supermanifolds and string fields in superstring theory, we construct new multilinear nonassociative products of forms which yield, for a single fermionic dimension, an $A_\infty $ algebra as in string field theory. For multiple fermionic directions, we give the rules for constructing nonassociative products, which are the basis for a full $A_\infty $ algebra structure to be yet discussed. […]

GUT Scale Unification in Heterotic Strings
by Angelantonj, Carlo on 18 December 2018 at 3:20
arXiv:1812.06915ARC1820Phys.Lett. B789 (2019) 496501by: Angelantonj, Carlo (Turin U.) et al.Abstract: We present a class of heterotic compactifications where it is possible to lower the string unification scale down to the GUT scale, while preserving the validity of the perturbative analysis. We illustrate this approach with an explicit example of a fourdimensional chiral heterotic vacuum with N=1 supersymmetry. […]

The Classical Solution for the Bosonic String in the Presence of Three Dbranes Rotated by Arbitrary SO(4) Elements
by Finotello, Riccardo on 13 December 2018 at 3:44
arXiv:1812.04643Nucl.Phys. B941 (2019) 158194by: Finotello, Riccardo (INFN, Turin) et al.Abstract: We consider the classical instantonic contribution to the open string configuration associated with three Dbranes with relative rotation matrices in SO(4) which corresponds to the computation of the classical part of the correlator of three non Abelian twist fields. We write the classical solution as a sum of a product of two hypergeometric functions. Differently from all the previous cases with three Dbranes, the solution is not holomorphic and suggests that the classical bosonic string knows when the configuration may be supersymmetric. We show how this configuration reduces to the standard Abelian twist field computation. From the phenomenological point of view, the Yukawa couplings between chiral matter at the intersection in this configuration are more suppressed with respect to the factorized case in the literature. […]

SUSY and the bivector
by Orlando, Domenico on 30 November 2018 at 3:25
arXiv:1811.11764Phys.Scripta 94 (2019) 095001by: Orlando, Domenico (Turin U.) et al.Abstract: In this note we give an explicit formula for the preserved Killing spinors in deformed string theory backgrounds corresponding to integrable Yang–Baxter deformations realized via (sequences of) TsT transformations. The Killing spinors can be expressed only in terms of the bivector Θ which encodes the deformation. This formula is applicable to deformed backgrounds related to rmatrices of various ranks, including those that do not satisfy the unimodularity condition and give rise to backgrounds in generalized supergravity. We conjecture that our formula also remains valid for integrable deformations which are not realized via TsT transformations and motivate this conjecture by explicit examples. […]

History operators in quantum mechanics
by Castellani, Leonardo on 12 October 2018 at 2:08
arXiv:1810.03624ARC1806Int.J.Quant.Inf. 17 (2019) 1941001by: Castellani, LeonardoAbstract: It is convenient to describe a quantum system at all times by means of a "history operator" $C$, encoding measurements and unitary time evolution between measurements. These operators naturally arise when computing the probability of measurement sequences, and generalize the "sum over position histories " of the Feynman pathintegral. As we argue in the present note, this description has some computational advantages over the usual state vector description, and may help to clarify some issues regarding nonlocality of quantum correlations and collapse. A measurement on a system described by $C$ modifies the history operator, $C \rightarrow PC$, where $P$ is the projector corresponding to the measurement. We refer to this modification as "history operator collapse". Thus $C$ keeps track of the succession of measurements on a system, and contains all histories compatible with the results of these measurements. The collapse modifies the history content of $C$, and therefore modifies also the past (relative to the measurement), but never in a way to violate causality. Probabilities of outcomes are obtained as $Tr(C^\dagger P C)/Tr(C^\dagger C)$. A similar formula yields probabilities for intermediate measurements, and reproduces the result of the twovector formalism in the case of given initial and final states. We apply the history operator formalism to a few examples: entangler circuit, MachZehnder interferometer, teleportation circuit, threebox experiment. Not surprisingly, the propagation of coordinate eigenstates $q\rangle$ is described by a history operator $C$ containing the Feynman pathintegral. […]

The largecharge expansion for Schrödinger systems
by Favrod, Samuel on 19 September 2018 at 2:21
arXiv:1809.06371JHEP 1812 (2018) 052by: Favrod, Samuel (Zurich, ETH) et al.Abstract: In this note, we perform the largecharge expansion for nonrelativistic systems with a global U(1) symmetry in 3 + 1 and 2 + 1 spacetime dimensions, motivated by applications to the unitary Fermi gas and anyons. These systems do not have full conformal invariance, but are invariant under the Schrödinger group. Also here, the lowenergy physics is encoded by a Goldstone boson which is due to the breaking of the global symmetry when fixing the charge. We find that in 2 + 1 dimensions and higher, there is a largecharge expansion in which quantum corrections are suppressed with respect to the nexttoleading order terms in the Lagrangian. We give the nexttoleadingorder expressions for the ground state energy and the speed of sound. […]

Global Seiberg–Witten Maps for $U(n)$Bundles on Tori and Tduality
by Aschieri, Paolo on 18 September 2018 at 9:34
arXiv:1809.05426Annales Henri Poincare 20 (2019) 31973227by: Aschieri, Paolo (Piemonte Orientale U., Alessandria) et al.Abstract: Seiberg–Witten maps are a wellestablished method to locally construct noncommutative gauge theories starting from commutative gauge theories. We revisit and classify the ambiguities and the freedom in the definition. Geometrically, Seiberg–Witten maps provide a quantization of bundles with connections. We study the case of U(n)vector bundles on twodimensional tori, prove the existence of globally defined Seiberg–Witten maps (induced from the plane to the torus) and show their compatibility with Morita equivalence. […]

Superstring Field Theory, Superforms and Supergeometry
by Catenacci, R. on 26 July 2018 at 3:33
arXiv:1807.09563DISIT18ARC1805J.Geom.Phys. 148 (2020) 103559by: Catenacci, R. (Piemonte Orientale U., Alessandria) et al.Abstract: Inspired by superstring field theory, we study differential, integral, and inverse forms and their mutual relations on a supermanifold from a sheaftheoretical point of view. In particular, the formal distributional properties of integral forms are recovered in this scenario in a geometrical way. Further, we show how inverse forms extend the ordinary de Rham complex on a supermanifold, thus providing a mathematical foundation of the Large Hilbert Space used in superstrings. Last, we briefly discuss how the Hodge diamond of a supermanifold looks like, and we explicitly compute it for super Riemann surfaces. […]

Surface operators, dual quivers and contours
by Ashok, S.K. on 18 July 2018 at 2:24
arXiv:1807.06316Eur.Phys.J. C79 (2019) 278by: Ashok, S.K. (IMSc, Chennai) et al.Abstract: We study halfBPS surface operators in four dimensional ${{{\mathcal {N}}}}=2$ SU(N) gauge theories, and analyze their lowenergy effective action on the four dimensional Coulomb branch using equivariant localization. We also study surface operators as coupled 2d/4d quiver gauge theories with an SU(N) flavour symmetry. In this description, the same surface operator can be described by different quivers that are related to each other by two dimensional Seiberg duality. We argue that these dual quivers correspond, on the localization side, to distinct integration contours that can be determined by the FayetIliopoulos parameters of the two dimensional gauge nodes. We verify the proposal by mapping the solutions of the twisted chiral ring equations of the 2d/4d quivers onto individual residues of the localization integrand. […]

The Gauge Group of a Noncommutative Principal Bundle and Twist Deformations
by Aschieri, Paolo on 6 June 2018 at 15:50
arXiv:1806.01841by: Aschieri, PaoloAbstract: We study noncommutative principal bundles (HopfGalois extensions) in the context of coquasitriangular Hopf algebras and their monoidal category of comodule algebras. When the total space is quasicommutative, and thus the base space subalgebra is central, we define the gauge group as the group of vertical automorphisms or equivalently as the group of equivariant algebra maps. We study Drinfeld twist (2cocycle) deformations of HopfGalois extensions and show that the gauge group of the twisted extension is isomorphic to the gauge group of the initial extension. In particular noncommutative principal bundles arising via twist deformation of commutative principal bundles have classical gauge group. We illustrate the theory with a few examples. […]

Killing spinors from classical $r$matrices
by Orlando, Domenico on 4 May 2018 at 2:03
arXiv:1805.00948KUNS2731J.Phys. A51 (2018) 395401by: Orlando, Domenico (INFN, Turin) et al.Abstract: The Yang–Baxter deformation (yb deformation) is a systematic way of performing integrable deformations of 2D symmetric nonlinear sigma models. The deformations can be labeled by classical rmatrices satisfying the classical yb equation. This yb deformation is also applicable to type IIB superstring theory defined on AdS. In this case, a simple class of yb deformations is associated with TsT transformations of string backgrounds. The data of this transformation is encoded in an antisymmetric bivector Θ (which is often called β field or noncommutativity parameter). In this article, we give a simple recipe for obtaining the explicit expression for the Killing spinors of the TsT transformed background starting from Θ. We moreover discuss the Mtheory equivalent of the TsT transformation, allowing us to also give Killing spinors of 11D backgrounds. We discuss examples of TsT transformed backgrounds starting from flat space, and . We find that in this way we can relate the Ωdeformation to yb deformations. […]

An AdS/EFT correspondence at large charge
by Loukas, Orestis on 13 April 2018 at 2:47
arXiv:1804.04151Nucl.Phys. B934 (2018) 437458by: Loukas, Orestis (U. Bern, AEC) et al.Abstract: Considering theories in sectors of large global charge Q results in a semiclassical effective field theory ( eft ) description for some stronglycoupled conformal field theories ( cfts ) with continuous global symmetries. Hence, when studying dualities at large charge, we can have control over the strongly coupled side of the duality and gain perturbative access to both dual pairs. […]

Universal correlation functions in rank 1 SCFTs
by Hellerman, Simeon on 6 April 2018 at 2:45
arXiv:1804.01535CALTTH2018014IPMU180059JHEP 1912 (2019) 047by: Hellerman, Simeon (Tokyo U., IPMU) et al.Abstract: Carrying to higher precision the large$ \mathcal{J} $ expansion of [1], we calculate to all orders in $ 1/\mathcal{J} $ the powerlaw corrections to the twopoint functions $ {\mathcal{Y}}_n\equiv {\leftxy\right}^{2n{\varDelta\mathcal{O}}}\cdot \le \left\langle {\mathcal{O}}^n(x){\overline{\mathcal{O}}}^n(y)\right\rangle $ for generators $ \mathcal{O} $ of Coulomb branch chiral rings in fourdimensional $ \mathcal{N}=2 $ superconformal field theories. We show these correlators have the universal largen expansion […]

$N=2^∗$ (non)Abelian theory in the $\Omega$ background from string theory
by Samsonyan, Marine on 29 March 2018 at 10:13
PoS EPSHEP2017 (2017) 546by: Samsonyan, Marine (CERN) et al.Abstract: We present a Dbrane realisation of the Abelian and nonAbelian N = 2 ∗ theory both in five and four dimensions. We compute topological amplitudes in string theory for Ω deformed spacetime first with one and then with two parameters. In the field theory limit we recover the perturbative partition function of the deformed N = 2 ∗ theory in agreement with the existing literature. […]

Extended Gauge Theory Deformations From~Flux~Backgrounds
by Lambert, Neil on 19 March 2018 at 2:39
arXiv:1803.05916JHEP 1806 (2018) 136by: Lambert, Neil (King's Coll. London, Dept. Math) et al.Abstract: We consider supersymmetric deformations of gauge theories in various dimensions obtained from a String Theory realisation of branes embedded in flux backgrounds. In particular we obtain deformations which take the form of Wilson line defects, also obtained by a twisting of the Rsymmetry into the gauge symmetry. Furthermore we construct higherorder generalisations, also expressed a twisting of the Rsymmetry, that have symmetries associated to codimension two and three defects. […]

Correlators between Wilson loop and chiral operators in $ \mathcal{N}=2 $ conformal gauge theories
by Billo, M. on 28 February 2018 at 3:21
ARC1803arXiv:1802.09813JHEP 1803 (2018) 193by: Billo, M. (Turin U.) et al.Abstract: We consider conformal N=2 super YangMills theories with gauge group SU(N) and Nf=2N fundamental hypermultiplets in presence of a circular 1/2BPS Wilson loop. It is natural to conjecture that the matrix model which describes the expectation value of this system also encodes the onepoint functions of chiral scalar operators in presence of the Wilson loop. We obtain evidence of this conjecture by successfully comparing, at finite N and at the twoloop order, the onepoint functions computed in field theory with the vacuum expectation values of the corresponding normalordered operators in the matrix model. For the part of these expressions with transcendentality zeta(3), we also obtain results in the largeN limit that are exact in the 't Hooft coupling lambda. […]

Supergravity in the Group‐Geometric Framework: A Primer
by Castellani, Leonardo on 13 February 2018 at 3:19
arXiv:1802.03407ARC1802Fortsch.Phys. 66 (2018) 1800014by: Castellani, Leonardo (Piemonte Orientale U., Alessandria)Abstract: We review the group‐geometric approach to supergravity theories, in the perspective of recent developments and applications. Usual diffeomorphisms, gauge symmetries and supersymmetries are unified as superdiffeomorphisms in a supergroup manifold. Integration on supermanifolds is briefly revisited, and used as a tool to provide a bridge between component and superspace actions. As an illustration of the constructive techniques, the cases of off‐shell supergravities and Chern‐Simons supergravity are discussed in detail. A cursory account of supergravity is also included. We recall a covariant canonical formalism, well adapted to theories described by Lagrangians d‐forms, that allows to define a form hamiltonian and to recast constrained hamiltonian systems in a covariant form language. Finally, group geometry and properties of spinors and gamma matrices in dimensions are summarized in Appendices. […]

Unconventional supersymmetry at the boundary of AdS$_{4}$ supergravity
by Andrianopoli, L. on 25 January 2018 at 5:15
arXiv:1801.08081JHEP 1804 (2018) 007by: Andrianopoli, L. (Turin Polytechnic) et al.Abstract: In this paper we perform, in the spirit of the holographic correspondence, a particular asymptotic limit of N=2, AdS_4 supergravity to N=2 supergravity on a locally AdS_3 boundary. Our boundary theory enjoys OSp(22) x SO(1,2) invariance and is shown to contain the D=3 superChern Simons OSp(22) theory considered in [Alvarez:2011gd] and featuring "unconventional local supersymmetry". The model constructed in that reference describes the dynamics of a spin1/2 Dirac field in the absence of spin 3/2 gravitini and was shown to be relevant for the description of graphene, near the Dirac points, for specific spatial geometries. Our construction yields the model in [Alvarez:2011gd] with a specific prescription on the parameters. In this framework the Dirac spin1/2 fermion originates from the radial components of the gravitini in D=4. […]

Localization of effective actions in open superstring field theory
by Maccaferri, Carlo on 24 January 2018 at 2:21
arXiv:1801.07607JHEP 1803 (2018) 112by: Maccaferri, Carlo (INFN, Turin) et al.Abstract: We consider the construction of the algebraic part of Dbranes treelevel effective action from Berkovits open superstring field theory. Applying this construction to the quartic potential of massless fields carrying a specific worldsheet charge, we show that the full contribution to the potential localizes at the boundary of moduli space, reducing to elementary twopoint functions. As examples of this general mechanism, we show how the YangMills quartic potential and the instanton effective action of a Dp/D(p − 4) system are reproduced. […]

String Sigma Models on Curved Supermanifolds
by Catenacci, Roberto on 16 January 2018 at 4:58
ARC1801arXiv:1801.04854Universe 4 (2018) 60by: Catenacci, Roberto (Rome U.) et al.Abstract: We use the techniques of integral forms to analyse the easiest example of two dimensional sigma models on a supermanifold. We write the action as an integral of a top integral form over a D=2 supermanifold and we show how to interpolate between different superspace actions. Then, we consider curved supermanifolds and we show that the definitions used for flat supermanifold can also be used for curved supermanifolds. We prove it by first considering the case of a curved rigid supermanifold and then the case of a generic curved supermanifold described by a single superfield $E$. […]

Surface operators in 5d gauge theories and duality relations
by Ashok, S.K. on 20 December 2017 at 5:57
arXiv:1712.06946ARC1712JHEP 1805 (2018) 046by: Ashok, S.K. (IMSc, Chennai) et al.Abstract: We study halfBPS surface operators in 5d $ \mathcal{N} $ = 1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that governs the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations, we obtain constraints on the 3d and 5d ChernSimons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the ChernSimons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by AharonySeiberg dualities. […]

NonPerturbative aspects of Supersymmetric Gauge Theories with surface operators
by Rajan John, Renjan on 19 December 2017 at 6:38
by: Rajan John, Renjan (Chennai Math. Inst.)Abstract: In this thesis, we study gauge theories with N = 2 supersymmetry in four dimensions. The low energy effective action of these theories on their Coulomb branch is described by a holomorphic function called the prepotential. In the first half, we study linear conformal quiver theories with gauge group SU(2). These theories have an SU(2) gauge group at each node of the quiver, and matter arranged in the fundamental and the bifundamental representations, such that at each node the betafunction vanishes. To compute the prepotential for these theories, we follow three different approaches. These are (i) the classic SeibergWitten approach, in which we consider an Mtheory construction of the SeibergWitten curve and the associated differential, (ii) equivariant localization as developed by Nekrasov, and (iii) the 2d/4d correspondence of the four dimensional gauge theory with the two dimensional Liouville conformal field theory, as put forward by Alday, Gaiotto, and Tachikawa. Matching the prepotential, we find out the precise map between the various parameters that appear in the three descriptions. In the latter half of the thesis, we study surface operators in the context of N=2* theories with gauge group SU(N). These theories describe the dynamics of a vector multiplet, and a massive hypermultiplet in the adjoint representation of the gauge group. Surface operators are nonlocal operators that have support on a two dimensional submanifold of the four dimensional spacetime. They are defined by the singularities they induce in the fourdimensional gauge fields, or can be characterized by the twodimensional theory they support on their worldvolume. The infrared dynamics on the worldvolume of the twodimensional surface operator is described by a holomorphic function called the twisted superpotential. Using localization techniques, we obtain the instanton partition function, and thereby the twisted superpotential of these theories. This involves taking a suitable orbifold of the original action without the surface operator. Imposing constraints from Sduality, we obtain a modular anomaly equation for the coefficients that appear in the mass expansion of the twisted superpotential. Solving the modular anomaly equation at each order, and comparing with the results obtained from localization, we resum the twisted superpotential in a mass series, whose coefficient functions depend on (quasi) modular forms and elliptic functions of the bare coupling constant and the continuous (complex) parameters that describe the surface operator. We further show that our results for monodromy defects in the fourdimensional theory, match the effective twisted superpotential that describes the infrared properties of certain two dimensional sigma models couples to N=2* gauge theories. This provides strong evidence for the proposed duality between the two descriptions. […]

WessZumino and Super YangMills Theories in D=4 Integral Superspace
by Castellani, L. on 21 November 2017 at 5:10
DISIT2017YITP1768ARC1709arXiv:1711.07194JHEP 1805 (2018) 040JHEP 1807 (2018) 175by: Castellani, L. (Piemonte Orientale U., Alessandria) et al.Abstract: We reconstruct the action of $N=1, D=4$ WessZumino and $N=1, 2, D=4$ superYangMills theories, using integral top forms on the supermanifold ${\cal M}^{(44)}$. Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework. […]

Anomalous dimensions of spinning operators from conformal symmetry
by Gliozzi, Ferdinando on 16 November 2017 at 7:23
arXiv:1711.05530JHEP 1801 (2018) 113by: Gliozzi, Ferdinando (INFN, Turin)Abstract: We compute, to the first nontrivial order in the ϵexpansion of a perturbed scalar field theory, the anomalous dimensions of an infinite class of primary operators with arbitrary spin ℓ = 0, 1, . . . , including as a particular case the weakly broken higherspin currents, using only constraints from conformal symmetry. Following the bootstrap philosophy, no reference is made to any Lagrangian, equations of motion or coupling constants. Even the space dimensions d are left free. The interaction is implicitly turned on through the local operators by letting them acquire anomalous dimensions. […]

$\mathrm{D=10}$ SuperYangMills Theory and Poincar\'e Duality in Supermanifolds
by Fré, Pietro on 1 November 2017 at 5:48
YITP17114ARC1710arXiv:1710.11498by: Fré, Pietro (INFN, Turin) et al.Abstract: We consider super YangMills theory on supermanifolds $\mathcal{M}^{(Dm)}$ using integral forms. The latter are used to define a geometric theory of integration and are essential for a consistent action principle. The construction relies on Picture Changing Operators $\mathbb{Y}^{(0m)}$, analogous to those introduced in String Theory, that admit the geometric interpretation of Poincar\'e duals of closed submanifolds of superspace $\mathcal{S}^{(D0)} \subset \mathcal{M}^{(Dm)}$ having maximal bosonic dimension $D$. We discuss the case of SuperYangMills theory in $D=10$ with $\mathcal{N}=1$ supersymmetry and we show how to retrieve its purespinor formulation from the rheonomic lagrangian $\mathcal{L}_{rheo}$ of D'Auria, Fr\'e and Da Silva, choosing a suitable $\mathbb{Y}^{(0m)}_{ps}$. From the same lagrangian $\mathcal{L}_{rheo}$, with another choice $\mathbb{Y}^{(0m)}_{comp}$ of the PCO, one retrieves the component form of the SYM action. Equivalence of the formulations is ensured when the corresponding PCO.s are cohomologous, which is true, in this case, of $\mathbb{Y}^{(0m)}_{ps}$ and $\mathbb{Y}^{(0m)}_{comp}$. […]

Nonassociative differential geometry and gravity with nongeometric fluxes
by Aschieri, Paolo on 1 November 2017 at 5:48
EMPG1716arXiv:1710.11467JHEP 1802 (2018) 036by: Aschieri, Paolo (Piemonte Orientale U., Alessandria) et al.Abstract: We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally nongeometric closed string vacua, and use it to construct preliminary steps towards a nonassociative theory of gravity on spacetime. We obtain explicit expressions for the torsion, curvature, Ricci tensor and LeviCivita connection in nonassociative Riemannian geometry on phase space, and write down Einstein field equations. We apply this formalism to construct Rflux corrections to the Ricci tensor on spacetime, and comment on the potential implications of these structures in nongeometric string theory and double field theory. […]

Pinching parameters for open (super) strings
by Playle, Sam on 2 October 2017 at 3:27
arXiv:1709.10117JHEP 1802 (2018) 093by: Playle, Sam (INFN, Turin) et al.Abstract: We present an approach to the parametrization of (super) Schottky space obtained by sewing together threepunctured discs with strips. Different cubic ribbon graphs classify distinct sets of pinching parameters, we show how they are mapped onto each other. The parametrization is particularly wellsuited to describing the region within (super) moduli space where open bosonic or NeveuSchwarz string propagators become very long and thin, which dominates the IR behaviour of string theories. We show how worldsheet objects such as the Green’s function converge to graph theoretic objects such as the Symanzik polynomials in the α$^{′}$ → 0 limit, allowing us to see how string theory reproduces the sum over Feynman graphs. The (super) string measure takes on a simple and elegant form when expressed in terms of these parameters. […]

Surface operators, chiral rings and localization in $ \mathcal{N} $ =2 gauge theories
by Ashok, S.K. on 28 July 2017 at 3:55
ARC175arXiv:1707.08922JHEP 1711 (2017) 137by: Ashok, S.K. (HBNI, Mumbai) et al.Abstract: We study halfBPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three dimensions, coupled respectively to four and fivedimensional gauge theories. The chiral ring equations, which arise from extremizing a twisted chiral superpotential, are solved as power series in the infrared scales of the quiver theories. In the second approach we use equivariant localization and obtain the twisted chiral superpotential as a function of the Coulomb moduli of the four and fivedimensional gauge theories, and find a perfect match with the results obtained from the chiral ring equations. In the fivedimensional case this match is achieved after solving a number of subtleties in the localization formulas which amounts to choosing a particular residue prescription in the integrals that yield the Nekrasovlike partition functions for ramified instantons. We also comment on the necessity of including ChernSimons terms in order to match the superpotentials obtained from dual quiver descriptions of a given surface operator. […]

Gauge supergravity in D = 2 + 2
by Castellani, Leonardo on 13 July 2017 at 4:16
ARC1704arXiv:1707.03411JHEP 1710 (2017) 062by: Castellani, Leonardo (Piemonte Orientale U., Alessandria)Abstract: We present an action for chiral N = (1, 0) supergravity in 2 + 2 dimensions. The fields of the theory are organized into an OSp(14) connection supermatrix, and are given by the usual vierbein V$^{a}$ , spin connection ω$^{ab}$ , and Majorana gravitino ψ. In analogy with a construction used for D = 10 + 2 gauge supergravity, the action is given by ∫STr(R$^{2}$ Γ), where R is the OSp(14) curvature supermatrix twoform, and Γ a constant supermatrix containing γ$_{5}$. It is similar, but not identical to the MacDowellMansouri action for D = 2 + 2 supergravity. The constant supermatrix breaks OSp(14) gauge invariance to a subalgebra OSp(12) ⊕ Sp(2), including a MajoranaWeyl supercharge. Thus half of the OSp(14) gauge supersymmetry survives. The gauge fields are the selfdual part of ω$^{ab}$ and the Weyl projection of ψ for OSp(12), and the antiselfdual part of ω$^{ab}$ for Sp(2). Supersymmetry transformations, being part of a gauge superalgebra, close offshell. The selfduality condition on the spin connection can be consistently imposed, and the resulting “projected” action is OSp(12) gauge invariant. […]

Matrix models at large charge
by Loukas, Orestis on 5 July 2017 at 4:17
arXiv:1707.00710JHEP 1710 (2017) 085by: Loukas, Orestis (Bern U.) et al.Abstract: We show that the largecharge formalism can be successfully applied to models that go beyond the vector models discussed so far in the literature. We study the explicit example of a conformal SU(3) matrix model in 2+1 spacetime dimensions at fixed charge and calculate the anomalous dimension and fusion coefficients at leading order in the U(1) charge. […]

Conformal dimensions via large charge expansion
by Banerjee, Debasish on 5 July 2017 at 4:13
arXiv:1707.00711Phys.Rev.Lett. 120 (2018) 061603by: Banerjee, Debasish (DESY, Zeuthen) et al.Abstract: We construct an efficient Monte Carlo algorithm that overcomes the severe signaltonoise ratio problems and helps us to accurately compute the conformal dimensions of largeQ fields at the WilsonFisher fixed point in the O(2) universality class. Using it, we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global U(1) charge can be obtained via a series expansion in the inverse charge 1/Q. We find that the conformal dimensions of the lowest operator with a fixed charge Q are almost entirely determined by the first few terms in the series. […]

Super Quantum Mechanics in the Integral Form Formalism
by Castellani, L. on 16 June 2017 at 4:15
(A)DISIT2017ARC1703YITP1752arXiv:1706.04704Annales Henri Poincare 19 (2018) 13851417by: Castellani, L. (Piemonte Orientale U., Alessandria) et al.Abstract: We reformulate superquantum mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of picture changing operators (PCO). In this way we retrieve component and superspace actions and prove their equivalence. The PCO are closed integral forms and can be interpreted as superPoincaré duals of bosonic submanifolds embedded into a supermanifold. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The $D=1, N=1$ and the $D=1, N=2$ cases are studied, in a flat and in a curved supermanifold. In this formalism, we also consider coupling with gauge fields, Hilbert space of quantum states, and observables. […]

Monopole Quivers and new 3D N=2 dualities
by Amariti, Antonio on 29 May 2017 at 2:53
arXiv:1705.09297Nucl.Phys. B924 (2017) 153177by: Amariti, Antonio (Bern U.) et al.Abstract: We present a new family of dualities for threedimensional gauge theories, motivated by the brane realization of the reduction of fourdimensional dualities on a circle. This family can be understood as a generalization of Aharony duality to quiver gauge theories whose nodes interact via monopole terms in the superpotential. We refer to this family of theories as monopole quivers. We corroborate the new dualities by checking the equivalence of the threesphere partition functions, obtained from the standard circle reduction of the fourdimensional superconformal index. As a special case, we recover some dualities recently discussed in the literature. […]

More on the Hidden Symmetries of 11D Supergravity
by Andrianopoli, Laura on 18 May 2017 at 4:40
arXiv:1705.06251Phys.Lett. B772 (2017) 578585by: Andrianopoli, Laura (INFN, Turin) et al.Abstract: In this paper we clarify the relations occurring among the osp(132) algebra, the M algebra and the hidden superalgebra underlying the Free Differential Algebra of D=11 supergravity (to which we will refer as DFalgebra) that was introduced in the literature by D'Auria and Frè in 1981 and is actually a (Lorentz valued) central extension of the M algebra including a nilpotent spinor generator, Q′ . We focus in particular on the 4form cohomology in 11D superspace of the supergravity theory, strictly related to the presence in the theory of a 3form A(3) . Once formulated in terms of its hidden superalgebra of 1forms, we find that A(3) can be decomposed into the sum of two parts having different grouptheoretical meaning: One of them allows to reproduce the FDA of the 11D Supergravity due to nontrivial contributions to the 4form cohomology in superspace, while the second one does not contribute to the 4form cohomology, being a closed 3form in the vacuum, defining however a one parameter family of trilinear forms invariant under a symmetry algebra related to osp(132) by redefining the spin connection and adding a new Maurer–Cartan equation. […]

Twopoint Correlators in N=2 Gauge Theories
by Billo, M. on 9 May 2017 at 4:52
arXiv:1705.02909Nucl.Phys. B926 (2018) 427466by: Billo, M. (INFN, Turin) et al.Abstract: We consider twopoint correlators in SU( N ) gauge theories on R4 with N=2 supersymmetry and Nf massless hypermultiplets in the fundamental representation. Using localization on S4 , we compute the leading perturbative corrections to the twopoint functions of chiral/antichiral operators made of scalar fields. The results are compared at two and three loops against direct field theory computations for some special operators whose correlators remain finite in perturbation theory at the specific loop order. In the conformal case, the match is shown up to two loops for a generic choice of operators and for arbitrary N . […]

The Integral Form of D=3 ChernSimons Theories Probing ${\mathbb C}^n/\Gamma$ Singularities
by Fré, P. on 3 May 2017 at 4:21
ARC1701YITP1748arXiv:1705.00752Fortsch.Phys. 65 (2017) 1700040by: Fré, P. (INFN, Turin) et al.Abstract: We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS4/CFT3 correspondence. From the structural viewpoint, we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kähler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS4/CFT3 correspondence and more generally of M2branes we emphasize the role of the Kähler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a noncompact Kähler quotient K4 of some flat variety with respect to a suitable group. The crepant resolutions of Cn/Γ singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 ChernSimons Theory supposedly dual to the corresponding M2brane solution. […]

A locally supersymmetric $SO(10,2)$ invariant action for $D=12$ supergravity
by Castellani, Leonardo on 3 May 2017 at 4:09
ARC1702arXiv:1705.00638JHEP 1706 (2017) 061by: Castellani, Leonardo (Turin U.)Abstract: We present an action for N = 1 supergravity in 10 + 2 dimensions, containing the gauge fields of the OSp(164) superalgebra, i.e. oneforms B$^{(}^{n}^{)}$ with n=1,2,5,6,9,10 antisymmetric D=12 Lorentz indices and a Majorana gravitino ψ. The vielbein and spin connection correspond to B$^{(1)}$ and B$^{(2)}$ respectively. The action is not gauge invariant under the full OSp(164) superalgebra, but only under a subalgebra $ \tilde{F} $ (containing the F algebra OSp(132)), whose gauge fields are B$^{(2)}$, B$^{(6)}$, B$^{(10)}$ and the Weyl projected Majorana gravitino $ \frac{1}{2}\left(1+{\Gamma}_{13}\right)\psi $ . Supersymmetry transformations are therefore generated by a MajoranaWeyl supercharge and, being part of a gauge superalgebra, close offshell. The action is simply ∫STr(R$^{6}$ Γ) where R is the OSp(164) curvature supermatrix twoform, and Γ is a constant supermatrix involving Γ$_{13}$ and breaking OSp(164) to its $ \tilde{F} $ subalgebra. The usual EinsteinHilbert term is included in the action. […]

Observables and dispersion relations in κMinkowski spacetime
by Aschieri, Paolo on 28 March 2017 at 4:22
arXiv:1703.08726JHEP 1710 (2017) 152by: Aschieri, Paolo (INFN, Turin) et al.Abstract: We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. […]

BCFT and OSFT moduli: an exact perturbative comparison
by Larocca, Pier Vittorio on 22 February 2017 at 5:22
arXiv:1702.06489Eur.Phys.J. C77 (2017) 806by: Larocca, Pier Vittorio (INFN, Turin) et al.Abstract: Starting from the pseudo ${\mathcal {B}}_0$ gauge solution for marginal deformations in OSFT, we analytically compute the relation between the perturbative deformation parameter $\tilde{\lambda }$ in the solution and the BCFT marginal parameter $\lambda $ , up to fifth order, by evaluating the Ellwood invariants. We observe that the microscopic reason why $\tilde{\lambda }$ and $\lambda $ are different is that the OSFT propagator renormalizes contactterm divergences differently from the contour deformation used in BCFT. […]

A string realisation of $\varOmega$deformed Abelian $\mathcal{N}=2^*$ theory
by Angelantonj, Carlo on 17 February 2017 at 5:01
CERNTH2017038arXiv:1702.04998Nucl.Phys. B923 (2017) 3253by: Angelantonj, Carlo (INFN, Turin) et al.Abstract: The N=2⁎ supersymmetric gauge theory is a massive deformation of N=4 , in which the adjoint hypermultiplet gets a mass. We present a Dbrane realisation of the (non)Abelian N=2⁎ theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higherdimensional operators in the effective supergravity action that involve powers of the antiselfdual N=2 chiral Weyl superfield and of selfdual gauge field strengths superpartners of the D5brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the twoparameter Ω background, in agreement with a recent proposal. […]

The analytic structure of conformal blocks and the generalized WilsonFisher fixed points
by Gliozzi, Ferdinando on 15 February 2017 at 5:08
CALTTH2017009arXiv:1702.03938JHEP 1704 (2017) 056by: Gliozzi, Ferdinando (Turin U.) et al.Abstract: We describe in detail the method used in our previous work arXiv:1611.10344 to study the WilsonFisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first nontrivial order in the ϵexpansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study singlescalar and O(N)invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to nonunitary theories as well. Some implications of our results for the study of the nonunitary theories containing partially conserved higherspin currents are briefly mentioned. […]

Modular and duality properties of surface operators in N=2* gauge theories
by Ashok, S.K. on 10 February 2017 at 4:55
arXiv:1702.02833JHEP 1707 (2017) 068by: Ashok, S.K. (HBNI, Mumbai) et al.Abstract: We calculate the instanton partition function of the fourdimensional $ \mathcal{N}={2}^{\star } $ SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from Sduality, we show that the effective twisted superpotential, which governs the infrared dynamics of the twodimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasimodular forms which resum all nonperturbative corrections. We also show that our results, derived for monodromy defects in the fourdimensional theory, match the effective twisted superpotential describing the infrared properties of certain twodimensional sigma models coupled either to pure $ \mathcal{N}=2 $ or to $ \mathcal{N}={2}^{\star } $ gauge theories. […]

On the gauge chosen by the bosonic open string
by Pesando, Igor on 30 January 2017 at 3:59
LAPTH00117arXiv:1701.07855Nucl.Phys. B918 (2017) 129161by: Pesando, Igor (Annecy, LAPTH)Abstract: String theory gives S matrix elements from which is not possible to read any gauge information. Using factorization we go off shell in the simplest and most naive way and we read which are the vertices suggested by string. To compare with the associated Effective Field Theory it is natural to use color ordered vertices. The α′=0 color ordered vertices suggested by string theory are more efficient than the usual ones since the three gluon color ordered vertex has three terms instead of six and the four gluon one has one term instead of three. They are written in the so called Gervais–Neveu gauge. The full Effective Field Theory is in a generalization of the Gervais–Neveu gauge with α′ corrections. Moreover a field redefinition is required to be mapped to the field used by string theory. […]