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Modular Bootstrap, Elliptic Points, and Quantum Gravity
by Gliozzi, Ferdinando on 2 August 2019 at 3:01
arXiv:1908.00029by: Gliozzi, FerdinandoAbstract: The modular bootstrap program for 2d CFTs could be seen as a systematic exploration of the physical consequences of consistency conditions at the elliptic points and at the cusp of their toruspartition function. The study at $\tau=i$, the elliptic point stabilized by the modular inversion $S$, was initiated by Hellerman, who found a general upper bound for the most relevant scaling dimension $\Delta$. Likewise, analyticity at $\tau=i\infty$, the cusp stabilized by the modular translation $T$, yields an upper bound on the twist gap. Here we study consistency conditions at $\tau=\exp[2i\pi/3]$, the elliptic point stabilized by $S T$. 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:1907.07152ARC1908by: 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:1907.03759KUNS2767by: 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 $O(d,d;\mathbb{R})$ deformation preserves integrability. As an application we compute the Lax pairs for continuous families of deformations, such as $J\bar{J}$ 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 N=2 SYM theories
by Billò, M. on 18 June 2019 at 3:05
arXiv:1906.07085by: Billò, M. (Turin U.) et al.Abstract: We consider the 1/2 BPS circular Wilson loop in a generic 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 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 zeta(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:1905.00026by: 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:1901.00818ARC1814by: 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 an $A_\infty$algebra. […]

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 YangBaxter deformations realized via (sequences of) TsT transformations. The Killing spinors can be expressed only in terms of the bivector $\Theta$ which encodes the deformation. This formula is applicable to deformed backgrounds related to $r$matrices 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:1810.03624ARC1806by: 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 SeibergWitten maps for U(n)bundles on tori and Tduality
by Aschieri, Paolo on 18 September 2018 at 9:34
arXiv:1809.05426by: Aschieri, Paolo (Piemonte Orientale U., Alessandria) et al.Abstract: SeibergWitten 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, SeibergWitten 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 SeibergWitten 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:1807.09563DISIT18ARC1805by: 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. […]