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Localization of effective actions in open superstring field theory: small Hilbert space
by Maccaferri, Carlo on 14 May 2019 at 8:55
arXiv:1905.04958by: Maccaferri, CarloAbstract: 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 $\N=2$ $R$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:1903.04431ARC1818by: Andrianopoli, L. (Turin Polytechnic) et al.Abstract: We consider $AdS_3$ $N$extended ChernSimons supergravity (\`a la AchucarroTonswend) 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:1902.09542by: 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 $(j_L, j_R)$. Using effective field theory we derive a formula for the conformal dimensions $D(j_L, j_R)$ of the leading operator in terms of two constants, $c_{3/2}$ and $c_{1/2}$, when the sum $j_L + j_R$ is much larger than the difference $j_Lj_R$. We compute $D(j_L,j_R)$ when $j_L = j_R$ 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 $c_{3/2}=1.068(4)$ and $c_{1/2}=0.083(3)$. […]

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:1902.01060by: 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 $N=$ 2 Gauge Theories. II
by Billo, M. on 29 January 2019 at 5:41
arXiv:1901.09693ROM2F/2019/02by: Billo, M. (Turin U.) et al.Abstract: We study the twopoint correlation functions of chiral/antichiral operators in $N=2$ supersymmetric YangMills theories on $R^4$ 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 $R^4$ are in perfect agreement with the same quantities computed using localization on the foursphere, even in the nonconformal case $N_f\not=2N$. […]

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:1901.08038by: Erler, Theodore (Prague, Inst. Phys.) et al.Abstract: Motivated by difficulties with 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 factorized tachyon vacuum in the $KBc$ subalgebra. We articulate sufficient conditions on the choice of tachyon vacuum to ensure the absence of ambiguous products in the equations of motion. Interestingly, the generalized solution can be obtained by appropriately enlarging the wellknown $KBc$ automorphisms to operate on boundary condition changing operators. […]

$A_\infty$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:1811.11764by: 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. […]

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:1804.01535CALTTH2018014IPMU180059by: Hellerman, Simeon (Tokyo U., IPMU) et al.Abstract: Carrying to higher precision the large$\mathcal{J}$ expansion of Hellerman and Maeda, we calculate to all orders in $1/\mathcal{J}$ the powerlaw corrections to the twopoint functions $\mathcal{Y}_n \equiv x  y^{2n\Delta_{\mathcal{O}}} \langle {\mathcal{O}}_n(x) \bar{\mathcal{O}}_n(y) \rangle$ for generators $\mathcal{O}$ of Coulomb branch chiral rings in fourdimensional $\mathcal{N} =2$ superconformal field theories. We show these correlators have the universal large$n$ expansion \[ \log(\mathcal{Y}_n) \simeq \mathcal{J} \mathbf{A} + \mathbf{B} + \log(\Gamma( \mathcal{J} + \alpha + 1)) , \] where $\mathcal{J} \equiv 2 n \Delta_{\mathcal{O}}$ is the total $R$charge of $\mathcal{O}_n$, the $\mathbf{A}$ and $\mathbf{B}$ are theorydependent coefficients, $\alpha$ is the coefficient of the WessZumino term for the Weyl $a$anomaly, and the $\simeq$ denotes equality up to terms exponentially small in $\mathcal{J}$. Our methods combine the structure of the Coulombbranch effective field theory (EFT) with the supersymmetric recursion relations. However, our results constrain the powerlaw corrections to all orders, even for nonLagrangian theories to which the recursion relations do not apply. For the case of $\mathcal{N} = 2$ SQCD, we also comment on the nature of the exponentially small corrections, which can be calculated to high precision in the doublescaling limit recently discussed by Bourget et al. We show the exponentially small correction is consistent with the interpretation of the EFT breaking down due to the propagation of massive BPS particles over distances of order of the infrared scale $x  y$. […]

$N=2^∗$ (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
ARC1802arXiv:1802.03407Fortsch.Phys. 66 (2018) 1800014by: Castellani, Leonardo (Piemonte Orientale U., Alessandria)Abstract: We review the groupgeometric 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 $d=3,4$ offshell supergravities and $d=5$ ChernSimons supergravity are discussed in detail. A cursory account of $d=10+2$ 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 $d=s+t$ dimensions are summarized in Appendices. […]