Non-relativistic duality and $T \bar T$ deformations

Brief lectures on duality, integrability and deformations

We provide a pedagogical introduction to some aspects of integrability, dualities and deformations of physical systems in 0+1 and in 1+1 dimensions. In particular, we concentrate on the T-duality of point particles and strings as well as on the Ruijsenaars duality of finite many-body integrable models, we review the concept of the integrability and, in particular, of the Lax integrability and we analyze the basic examples of the Yang-Baxter deformations of non-linear sigma-models. The central mathematical structure which we describe in detail is the E-model which is the dynamical system exhibi…

Induced deformation of the canonical structure and UV/IR duality in $(1+1)D$

The purpose of this work is two fold. Working in the framework of $(1+1)D$ Lorentz violating field theories we will investigate in the first place the general claim that fermionic interactions may be equivalent to a deformation of the canonical structure of the theory. Second the deformed theory will be studied using duality reasoning to address the behavior of the Infra-Red and Ultra-Violet regimes.

On quantum compatibility of counterterm deformations and duality symmetries in ${\cal N}\geq 5$ supergravities

In ${\cal N}=5, 6, 8$ supergravities there are hidden symmetries of equations of motion, described by duality groups $SU(1,5), \, SO^*(12), \, E_{7(7)}$ respectively. UV divergences and known candidate counterterms violate the deformed duality symmetry current conservation. Extra higher derivative terms in the action are required to restore duality. We study the effect of a two-vector part of the counterterm for ${\cal N}\geq 5$ supergravities using the universality of the symplectic structure of extended supergravities. We construct a compact form of a deformed action with infinite number of …

广义$T\overline{T}$类形变在对偶不变非线性电动力学理论中的应用

Generalized $T\overline{T}$-like Deformations in Duality-Invariant Nonlinear Electrodynamic Theories

本研究提出高阶微扰方法，分类对偶不变非线性电动力学中的两类解，并确认无关与边缘算子引发的应力张量流的可交换性。

Mixed (open/closed) N=(2,2) string theory as an integrable deformation of self-duality

The exact effective field equations of motion, corresponding to the perturbative mixed theory of open and closed (2,2) world-sheet supersymmetric strings, are investigated. It is shown that they are only integrable in the case of an abelian gauge group. The gravitational equations are then stationary with respect to the Born-Infeld-type effective action.

An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills

We study relevant deformations of an N=1 superconformal theory which is an exactly marginal deformation of U(N) N=4 SUSY Yang-Mills. The resulting theory has a classical Higgs branch that is a complex deformation of the orbifold C^3/Z_n x Z_n that is a non-compact Calabi-Yau space with isolated conifold singularities. At these singular points in moduli space the theory exhibits a duality cascade and flows to a confining theory with a mass gap. By exactly solving the corresponding holomorphic matrix model we compute the exact quantum superpotential generated at the end of the duality cascade an…

On quantum deformations of $AdS_3 \times S^3 \times T^4$ and mirror duality

We consider various integrable two-parameter deformations of the $AdS_3 \times S^3 \times T^4$ superstring with quantum group symmetry. Working on the string worldsheet in light-cone gauge and to quadratic order in fermions, we obtain their common massive tree-level two-body S matrix, which matches the expansion of the conjectured exact $q$-deformed S matrix. We then analyze the behavior of the exact S matrix under mirror transformation -- a double Wick rotation on the worldsheet -- and find that it satisfies a mirror duality relation analogous to the distinguished $q$-deformed $AdS_5 \times S…

S-Duality and Modular Transformation as a non-perturbative deformation of the ordinary pq-duality

A recent claim that the S-duality between 4d SUSY gauge theories, which is AGT related to the modular transformations of 2d conformal blocks, is no more than an ordinary Fourier transform at the perturbative level, is further traced down to the commutation relation [P,Q]=-i\hbar between the check-operator monodromies of the exponential resolvent operator in the underlying Dotsenko-Fateev matrix models and beta-ensembles. To this end, we treat the conformal blocks as eigenfunctions of the monodromy check operators, what is especially simple in the case of one-point toric block. The kernel of th…

Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings

We perform non-abelian T-duality for a generic Green-Schwarz string with respect to an isometry (super)group G, and we derive the transformation rules for the supergravity background fields. Specializing to G bosonic, or G fermionic but abelian, our results reproduce those available in the literature. We discuss also continuous deformations of the T-dual models, obtained by adding a closed B-field before the dualization. This idea can also be used to generate deformations of the original (un-dualized) model, when the 2-cocycle identified from the closed B is invertible. The latter construction…

Generalised T-duality and Integrable Deformations

We review some recent developments in the construction of integrable $η$- and $λ$-deformations of the $AdS_5 \times S^5$ superstring. We highlight their link with Poisson-Lie T-duality.

S-Duality, Deconstruction and Confinement for a Marginal Deformation of N=4 SUSY Yang-Mills

We study an exactly marginal deformation of N=4 SUSY Yang-Mills with gauge group U(N) using field theory and string theory methods. The classical theory has a Higgs branch for rational values of the deformation parameter. We argue that the quantum theory also has an S-dual confining branch which cannot be seen classically. The low-energy effective theory on these branches is a six-dimensional non-commutative gauge theory with sixteen supercharges. Confinement of magnetic and electric charges, on the Higgs and confining branches respectively, occurs due to the formation of BPS-saturated strings…

$\mathcal N=2$ Supersymmetry Deformations, Electromagnetic Duality and Dirac-Born-Infeld Actions

We study the general deformation of $\mathcal N=2$ supersymmetry transformations of a vector multiplet that forms a (constant) triplet under the $SU(2)$ R-symmetry corresponding to the magnetic dual of the triplet of the Fayet-Iliopoulos (FI) parameters. We show that in the presence of both triplets, the induced scalar potential of a vector multiplet with generic prepotential has always a minimum that realises partial breaking of $\mathcal N=2\to \mathcal N=1$ supersymmetry. We then consider the impact of the deformation in the Dirac-Born-Infeld (DBI) action where one supersymmetry is non-line…

S-duality of the Leigh-Strassler Deformation via Matrix Models

We investigate an exactly marginal N=1 supersymmetric deformation of SU(N) N=4 supersymmetric Yang-Mills theory discovered by Leigh and Strassler. We use a matrix model to compute the exact superpotential for a further massive deformation of the U(N) Leigh-Strassler theory. We then show how the exact superpotential and eigenvalue spectrum for the SU(N) theory follows by a process of integrating-in. We find that different vacua are related by an action of the SL(2,Z) modular group on the bare couplings of the theory extending the action of electric-magnetic duality away from the N=4 theory. We …

On non-abelian T-duality and deformations of supercoset string sigma-models

We elaborate on the class of deformed T-dual (DTD) models obtained by first adding a topological term to the action of a supercoset sigma model and then performing (non-abelian) T-duality on a subalgebra $\tilde{\mathfrak{g}}$ of the superisometry algebra. These models inherit the classical integrability of the parent one, and they include as special cases the so-called homogeneous Yang-Baxter sigma models as well as their non-abelian T-duals. Many properties of DTD models have simple algebraic interpretations. For example we show that their (non-abelian) T-duals---including certain deformatio…

Quantum properties and generalised T-duality of the Yang-Baxter Wess-Zumino model

In this short proceedings we discuss some of the results obtained in [1]. Integrable deformations enlarge the landscape and understanding of integrable models and its algebraic structures like quantum groups. In this short proceedings, we will review the one-loop renormalisation group analysis of an integrable deformation known as the Yang-Baxter Wess-Zumino model. This classically integrable model shows a striking stability under one-loop renormalisation. In addition, we show how Poisson-Lie T-duality, a generalisation of T-duality that is closely intertwined with integrable deformations, is …

Supersymmetry constraints on U-duality invariant deformations of $N \geq 5$ Supergravity

Candidate counterterms break E7 type U-duality symmetry of $N \geq 5$ supergravity theories in four dimensions \cite{Kallosh:2011dp}. A proposal was made in \cite{Bossard:2011ij} to restore it, starting with a double set of vector fields and argued that a supersymmetric extension of their proposal should exist. We show that the extra vectors, needed for the deformation, can not be auxiliary fields in an eventual off-shell formulation $N \geq 5$ supergravity, assuming that such a formulation exists. Furthermore we show that these extra vector fields can not be dynamical either since that change…

AGT on the S-duality Wall

Three-dimensional gauge theory T[G] arises on a domain wall between four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L. We argue that the N=2^* mass deformation of the bulk theory induces a mass-deformation of the theory T[G] on the wall. The partition functions of the theory T[SU(2)] and its mass-deformation on the three-sphere are shown to coincide with the transformation coefficient of Liouville one-point conformal block on torus under the S-duality.

Non-compact Mirror Bundles and (0,2) Liouville Theories

We study (0,2) deformations of N=2 Liouville field theory and its mirror duality. A gauged linear sigma model construction of the ultraviolet theory connects (0,2) deformations of Liouville field theory and (0,2) deformations of N=2 SL(2,R)/U(1) coset model as a mirror duality. Our duality proposal from the gauged linear sigma model completely agrees with the exact CFT analysis. In the context of heterotic string compactifications, the deformation corresponds to the introduction of a non-trivial gauge bundle. This non-compact Landau-Ginzburg construction yields a novel way to study the gauge b…

BPS States in the Duality Web of the Omega deformation

In this note, we study different limits of an Omega-deformed (2,0) six-dimensional gauge theory realized in a M-theory fluxtrap background. Via a chain of dualities, we connect the Omega-deformed SYM to a new four-dimensional gauge theory which we refer to as the reciprocal gauge theory. This theory has several properties in common with Liouville field theory, such as its gauge coupling b^2 =ε_2 / ε_1, and its behavior under S-duality. Finally, we realize the BPS states on the SYM side of the AGT correspondence and follow them along the chain of dualities. In the fluxtrap frame, we are dealing…

A Defect in AdS3/CFT2 Duality

$AdS_3$ string theory in the stringy regime $k=(R_{AdS}/\ell_{str})^2 < 1$ provides a laboratory for the study of holography in which both sides of AdS/CFT duality are under fairly good control. Worldsheet string theory is solvable, and for closed strings the dual spacetime CFT is a deformation of a symmetric product orbifold. Here we extend this construction to include open strings by adding a probe D-string, described semi-classically by an $AdS_2$ D-brane in $AdS_3$. The dual defect or boundary conformal field theory (BCFT) is again a deformed symmetric product, which now describes the Fock…

A note on "gaugings" in four spacetime dimensions and electric-magnetic duality

The variety of consistent "gauging" deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions. Ignoring supersymmetry we consider in this paper $n_v$ abelian vector potentials in four spacetime dimensions with non-minimal kinetic coupling to $n_s$ uncharged (possibly nonlinear) scalar fields. As in the case of extended supergravities, one model may possess different formulations related by $Sp(2n_v,\mathbb{R})$. The symplectic group mixes its electric and…

SYK/AdS duality with Yang-Baxter deformations

In this paper, based on the notion of SYK/AdS duality we explore the effects of Yang-Baxter (YB) deformations on the SYK spectrum at strong coupling. In the first part of our analysis, we explore the consequences of YB deformations through the Kaluza-Klein (KK) reduction on $ (AdS_2)_η\times (S^1)/Z_2 $. It turns out that the YB effects (on the SYK spectrum) starts showing off at \textit{quadratic} order in $ 1/J $ expansion. For the rest of the analysis, we provide an interpretation for the YB deformations in terms of bi-local/collective field excitations of the SYK model. Using large $ N $ t…

最小形变下的色-运动学对偶：重访纯杨-米尔斯理论中的双圈四胶子振幅

Color-Kinematics Duality with Minimal Deformation: Two-Loop Four-Gluon Amplitudes in Pure Yang-Mills Revisited

本文通过引入满足离壳对偶雅可比关系子集的最小形变，解决了纯杨-米尔斯理论双圈四胶子振幅中构造色-运动学对偶分子的难题，所得d维洛伦兹不变局域分子适用于所有螺旋度，并可直接用于双拷贝构造引力振幅。

Unimodular jordanian deformations of integrable superstrings

We find new homogeneous r matrices containing supercharges, and use them to find new backgrounds of Yang-Baxter deformed superstrings. We obtain these as limits of unimodular inhomogeneous r matrices and associated deformations of AdS2 x S2 x T6 and AdS5 x S5. Our r matrices are jordanian, but also unimodular, and lead to solutions of the regular supergravity equations of motion. In general our deformations are equivalent to particular non-abelian T duality transformations. Curiously, one of our backgrounds is also equivalent to one produced by TsT transformations and an S duality transformati…

Axial Vector Duality as a Gauge Symmetry and Topology Change in String Theory

Lines generated by marginal deformations of WZW models are considered. The Weyl symmetry at the WZW point implies the existence of a duality symmetry on such lines. The duality is interpreted as a broken gauge symmetry in string theory. It is shown that at the two end points the axial and vector cosets are obtained. This shows that the axial and vector cosets are equivalent CFTs both in the compact and the non-compact cases. Moreover, it is shown that there are $\s$-model deformations that interpolate smoothly between manifolds with different topologies.

Self-dual Hamiltonians as Deformations of Free Systems

We formulate the problem of finding self-dual Hamiltonians (associated with integrable systems) as deformations of free systems given on various symplectic manifolds and discuss several known explicit examples, including recently found double elliptic Hamiltonians. We consider as basic the notion of self-duality, while the duality in integrable systems (of the Toda/Calogero/Ruijsenaars type) comes as a derivative notion (degenerations of self-dual systems). This is a talk presented at the Workshop "Classical and Quantum Integrable Systems", Protvino, January, 2001.

Electric-magnetic deformations of D=4 gauged supergravities

We discuss duality orbits and symplectic deformations of D=4 gauged supergravity theories, with focus on N$\ge$2. We provide a general constructive framework for computing symplectic deformations starting from a reference gauging, and apply it to many interesting examples. We prove that no continuous deformations are allowed for Fayet-Iliopoulos gaugings of the N=2 STU model and in particular that any $ω$ deformation is classically trivial. We further show that although in the N=6 truncation of SO(8) maximal supergravity the $ω$ parameter can be dualized away, in the 'twin' N=2 truncation $ω$ …

Numerical Loop-Tree Duality: contour deformation and subtraction

We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour deformation automatically satisfies all constraints without the need for fine-tuning. We demonstrate that our construction is systematic and efficient by applying it to more than 100 examples of finite scalar integrals featuring up to six loops. We also showcase a first step towards handling non-integrable singularities by applying our work to one-loop infrared…

T对偶与Sigma模型的类$T \overline{T}$形变

T-Duality and $T \overline{T}$-like Deformations of Sigma Models

该研究探讨二维sigma模型中T对偶与应力张量形变的相互作用，证明阿贝尔、非阿贝尔T对偶分别与$T\overline{T}$形变、类$T\overline{T}$流对易，且PCM及其T对偶的相关辅助场形变经典可积。

Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory

We analyze in detail the relation between an exactly marginal deformation of N=4 SYM - the Leigh-Strassler or ``beta-deformation'' - and its string theory dual (recently constructed in hep-th/0502086) by comparing energies of semiclassical strings to anomalous dimensions of gauge-theory operators in the two-scalar sector. We stress the existence of integrable structures on the two sides of the duality. In particular, we argue that the integrability of strings in AdS_5 x S^5 implies the integrability of the deformed world sheet theory with real deformation parameter. We compare the fast string …

Obstruction to E_{7(7)} Deformation in N=8 Supergravity

Candidate counterterms break Noether-Gaillard-Zumino E_{7(7)} current conservation in N=8 supergravity in four dimensions. Bossard and Nicolai proposed a scheme for deforming the subsector involving vector fields in a Lorentz covariant manner, so as to restore duality. They argued that there must exist an extension of this deformation to the full theory that preserves supersymmetry. We show that it is not possible to deform the maximal supergravity to restore E_{7(7)} duality, while maintaining both general covariance and N=8 supersymmetry, as was proposed. Deformation of N=8 supergravity requ…

Electric-magnetic Duality and Deformations of Three-Dimensional CFT's

SL(2,Z) duality transformations in asymptotically AdS4 x S^7 act non-trivially on the three-dimensional SCFT of coincident M2-branes on the boundary. We show how S-duality acts away from the IR fixed point. We develop a systematic method to holographically obtain the deformations of the boundary CFT and show how electric-magnetic duality relates different deformations. We analyze in detail marginal deformations and deformations by dimension 4 operators. In the case of massive deformations, the RG flow relates S-dual CFT's. Correlation functions in the CFT are computed by varying magnetic bulk …

Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory

We consider a non-supersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS_5 x S5 by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters gamma_i which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as N=4 SYM theory, but with scalar and Yukawa interactions ``deformed'' by gamma_i-dependent phases. The special case of equal deformation para…

Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality

Based on the construction of Poisson-Lie T-dual $σ$-models from a common parent action we study a candidate for the non-abelian respectively Poisson-Lie T-duality group. This group generalises the well-known abelian T-duality group O(d,d) and we explore some of its subgroups, namely factorised dualities, B- and $β$-shifts. The corresponding duality transformed $σ$-models are constructed and interpreted as generalised (non-geometric) flux backgrounds. We also comment on generalisations of results and techniques known from abelian T-duality. This includes the Lie algebra cohomology interpretatio…

Two-loop conformal invariance for Yang-Baxter deformed strings

The so-called homogeneous Yang-Baxter (YB) deformations can be considered a non-abelian generalization of T-duality--shift--T-duality (TsT) transformations. TsT transformations are known to preserve conformal symmetry to all orders in $α'$. Here we argue that (unimodular) YB deformations of a bosonic string also preserve conformal symmetry, at least to two-loop order. We do this by showing that, starting from a background with no NSNS-flux, the deformed background solves the $α'$-corrected supergravity equations to second order in the deformation parameter. At the same time we determine the re…

$GL(2,\mathbb{R})$ WZW模型的Yang-Baxter形变与非阿贝尔T对偶

Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality

该研究通过计算gl(2,R)李代数的不等价经典r矩阵，将GL(2,R)上WZW模型的Yang-Baxter形变分为12族，证明所有形变模型均具Poisson-Lie对称性，可由含旁观场的Poisson-Lie T对偶σ模型得到，并给出一例的对偶背景。

Modular anomaly equation, heat kernel and S-duality in N=2 theories

We investigate epsilon-deformed N=2 superconformal gauge theories in four dimensions, focusing on the N=2* and Nf=4 SU(2) cases. We show how the modular anomaly equation obeyed by the deformed prepotential can be efficiently used to derive its non-perturbative expression starting from the perturbative one. We also show that the modular anomaly equation implies that S-duality is implemented by means of an exact Fourier transform even for arbitrary values of the deformation parameters, and then we argue that it is possible, perturbatively in the deformation, to choose appropriate variables such …

Warped AdS3/Dipole-CFT Duality

String theory contains solutions with SL(2,R)_R x U(1)_L-invariant warped AdS3 (WAdS3) factors arising as continuous deformations of ordinary AdS3 factors. We propose that some of these are holographically dual to the IR limits of nonlocal dipole-deformed 2D D-brane gauge theories, referred to as "dipole CFTs". Neither the bulk nor boundary theories are currently well-understood, and consequences of the proposed duality for both sides is investigated. The bulk entropy-area law suggests that dipole CFTs have (at large N) a high-energy density of states which does not depend on the deformation p…

An Introduction to Generalised Dualities and their Applications to Holography and Integrability

These pedagogical lectures given at the Corfu Summer Institute 2018 review two generalised notions of T-duality, non-Abelian T-duality and Poisson-Lie duality, and their applications. We explain how each of these has seen recent application in the context of holography. Non-Abelian T-duality has been used to construct new holographic dual geometries. Poisson-Lie duality has been used to construct new integrable string sigma-models including the $η$- and $λ$-deformations of the $AdS_5\times S^5$ superstring thought to encode quantum group deformations of holography. We also comment on the doubl…

Non-holomorphic deformations of special geometry and their applications

The aim of these lecture notes is to give a pedagogical introduction to the subject of non-holomorphic deformations of special geometry. This subject was first introduced in the context of N=2 BPS black holes, but has a wider range of applicability. A theorem is presented according to which an arbitrary point-particle Lagrangian can be formulated in terms of a complex function F, whose features are analogous to those of the holomorphic function of special geometry. A crucial role is played by a symplectic vector that represents a complexification of the canonical variables, i.e. the coordinate…

AdS/CFT Duality for Non-Anticommutative Supersymmetric Gauge Theory

We construct type IIB supergravity duals of non-anticommutative deformed N = 4 SU(N) gauge theories. We consider in particular deformations preserving N = (1,0) and N = (1/2,0) supersymmetry. Such theories can be realised on N D3-branes in specific self-dual 5-form backgrounds. We show that the required 5-form field strengths can be produced by configurations of intersecting D3-branes and we are then able to construct the supergravity solutions in the near-horizon limit. We consider some consequences of this duality, in particular showing that the gravity duals predict that the dimensions of a…

Integrable supersymmetric deformations of $\rm AdS_3 \times S^3 \times T^4$

We construct a family of type IIB string backgrounds that are deformations of $\rm AdS_3 \times S^3 \times T^4$ with a "squashed" $\rm AdS_3 \times S^3$ metric supported by a combination of NSNS and RR fluxes. They have global $\rm SU(1,1) \times SU(2)$ symmetry, regular curvature, constant dilaton and preserve 8 supercharges. Upon compactification to 4 dimensions they reduce to $\mathcal N=2$ supersymmetric $\rm AdS_2 \times S^2$ solutions with electric and magnetic Maxwell fluxes. These type IIB supergravity solutions can be found from the undeformed $\rm AdS_3 \times S^3 \times T^4$ backgro…

Poisson-Lie T-Duality beyond the classical level and the renormalization group

In order to study quantum aspects of $\s$-models related by Poisson--Lie T-duality, we construct three- and two-dimensional models that correspond, in one of the dual faces, to deformations of $S^3$ and $S^2$. Their classical canonical equivalence is demonstrated by means of a generating functional, which we explicitly compute. We examine how they behave under the renormalization group and show that dually related models have the same 1-loop beta functions for the coupling and deformation parameters. We find non-trivial fixed points in the ultraviolet, where the theories do not become asymptot…

String spectrum of curved string backgrounds obtained by T-duality and shifts of polar angles

A class of exactly solvable string models can be obtained by starting with flat space and combining T-duality and shifts of angular coordinates of several polar planes. The models are the analog of the Lunin-Maldacena β-deformation of the AdS_5 x S^5 type IIB string background, which is dual to a Leigh-Strassler deformation of \N=4 Super Yang-Mills Theory. We determine the complete physical string spectrum for two string models obtained in this way, by explicitly solving the string equations and quantizing in terms of free creation and annihilation operators. We also show that the 3-parameter …

在三圈纯杨-米尔斯理论中应用色-运动学对偶

Applying Color-Kinematics Duality in Pure Yang-Mills at Three Loops

本文首次将色-运动学对偶应用于三圈纯杨-米尔斯理论，通过最小形变单个主分子式克服幺正切割困难，得到局域且洛伦兹不变的解，为构造三圈振幅和引力双拷贝提供新途径。

Supersymmetric $J\bar{T}$ and $T\bar{J}$ deformations

We explore the $J\bar{T}$ and $T\bar{J}$ deformations of two-dimensional field theories possessing $\mathcal N=(0,1),(1,1)$ and $(0,2)$ supersymmetry. Based on the stress-tensor and flavor current multiplets, we construct various bilinear supersymmetric primary operators that induce the $J\bar{T}/T\bar{J}$ deformation in a manifestly supersymmetric way. Moreover, their supersymmetric descendants are shown to agree with the conventional $J\bar T /T\bar J$ operator on-shell. We also present some examples of $J\bar T /T\bar J$ flows arising from the supersymmetric deformation of free theories. Fi…

Schwarzschild时空的共形超对称形变的超Poisson-Lie T-对偶/多重性分类

Classification of Conformal Supersymmetric Deformations of Schwarzschild Spacetime via Super Poisson-Lie T-duality/Plurality

本文通过超Poisson-Lie T-对偶/多重性框架，研究Schwarzschild时空的共形超对称形变，推导四维弦背景的共形对偶链，并分类超引力背景几何。

$T$-folds from Yang-Baxter deformations

Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local structure of the deformed geometries and the global structure still remains unclear. In this work, we reveal a non-geometric aspect of YB-deformed backgrounds as $T$-fold by explicitly showing the associated $\mathrm{O}(D,D;\mathbb{Z})$ $T$-duality monodromy. In particular, the appearance of an extra vector field in the generalized supergravity equations (GSE) leads to the non-geometric $Q$-flux. In addition, we stu…

Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation

Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of $SU(2)$ as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $\mathfrak{su}(2)(\mathbb{R}) \, \dot{\oplus} \, \mathfrak{a}$, to the fully semisimple Kac-Moody algebra $\mathfrak{sl}(2,\mathbb{C})(\mathbb{R})$. A two-parameter family of models with $SL(2,\mathbb{C})$ as target phase space is obtained so that Poisson-Lie T-duality is realised as an $O(3,3)$ rotation in the phase space. The dual family shares the same…

A Solvable Irrelevant Deformation of $AdS_3/CFT_2$

Recently we proposed a universal solvable irrelevant deformation of $AdS_3/CFT_2$ duality, which leads in the ultraviolet to a theory with a Hagedorn entropy [1]. In this note we provide a worldsheet description of this theory as a coset CFT, and compare its spectrum to the field theory predictions of [2,3].

On three-point correlation functions in the gauge/gravity duality

We study the effect of marginal and irrelevant deformations on the renormalization of operators near a CFT fixed point. New divergences in a given operator are determined by its OPE with the operator D that generates the deformation. This provides a scheme to compute the couplings a_DAB between the operator D and two arbitrary operators O_A and O_B. We exemplify for the case of N=4 SYM, considering the simplest case of the exact Lagrangian deformation. In this case the deformed anomalous dimension matrix is determined by the derivative of the anomalous dimension matrix with respect to the coup…

$T\bar{T}$ Deformations in Curved Space from 4D Chern-Simons Theory

In this paper, we shed new light onto $T\bar{T}$-deformations by engineering them on 2D surface defects, supporting chiral and antichiral CFT's, in a 4D Chern-Simons bulk. This approach is motivated by various connections between $T\bar{T}$-deformations, gravity and Chern-Simons theory and suggests that the formalism developed in this paper and the gravity picture of $T\bar{T}$-deformations should be closely related.

Heating up the Baryonic Branch with U-duality: a unified picture of conifold black holes

We study different aspects of a U-duality recently presented by Maldacena and Martelli and apply it to non-extremal backgrounds. In particular, starting from new non-extremal wrapped D5 branes we generate new non-extremal generalizations of the Baryonic Branch of the Klebanov-Strassler solution. We also elaborate on different conceptual aspects of these U-dualities, like its action on (extremal and non-extremal) Dp branes, dual models for Yang-Mills-like theories, generic asymptotics and decoupling limit of the generated solutions.

Chern Simons duality with a fundamental boson and fermion

We compute the thermal free energy for all renormalizable Chern Simon theories coupled to a single fundamental bosonic and fermionic field in the 't Hooft large N limit. We use our results to conjecture a strong weak coupling duality invariance for this class of theories. Our conjectured duality reduces to Giveon Kutasov duality when restricted to {\cal N}=2 supersymmetric theories and to an earlier conjectured bosonization duality in an appropriate decoupling limit. Consequently the bosonization duality may be regarded as a deformation of Giveon Kutasov duality, suggesting that it is true eve…