We construct a 1-parameter family of Ramond-Ramond fluxes supporting the elliptic AdS × S × T metric with constant dilaton and preserving 8 of the 16 supercharges of the undeformed background. On the supersymmetric locus, we compute the tree-level worldsheet S-matrix in uniform light-cone gauge up to quadratic order in fermions and find that it non-trivially satisfies the classical Yang-Baxter equation. Moreover, imposing classical integrability and symmetries, we conjecture compatible processes quartic in fermions. We also investigate different limits of interest, including trigonometric deformations and the limit to the AdS × S × T superstring. Our results provide strong evidence for a supersymmetric and integrable elliptic deformation of the AdS × S × T superstring supported by Ramond-Ramond flux and a constant dilaton.

United Kingdom

Ben Hoare

Germany

Switzerland

Fiona Seibold

Supersymmetry and integrability of the elliptic AdS3 $\textit{×}$ S3 $\textit{×}$ T4 superstring

We introduce the $\textit{ℤ}$ -twisted trigonometric sigma models, a new class of integrable deformations of the principal chiral model. Starting from 4d Chern-Simons theory on a cylinder, the models are constructed by introducing a $\textit{ℤ}$ branch cut running along the non-compact direction. As we pass through the branch cut we apply a $\textit{ℤ}$ automorphism to the algebra-valued and group-valued fields of the theory. Two instances of models in this class have appeared in the literature and we explain how these fit into our general construction. We generalise both to the case of $\textit{ℤ}$ -twistings, and for each we construct two further deformations, leading to four doubly-deformed models.

Rashad Hamidi

Twists of trigonometric sigma models

Recent work has shown that certain integrable and conformal field theories in two dimensions can be given a higher-dimensional origin from holomorphic Chern-Simons in six dimensions. Along with anti-self-dual Yang-Mills and four-dimensional Chern-Simons, this gives rise to a diamond correspondence of theories. In this work we extend this framework to incorporate models realised through gaugings. As well as describing a higher-dimensional origin of coset CFTs, by choosing the details of the reduction from higher dimensions, we obtain rich classes of two-dimensional integrable models including homogeneous sine-Gordon models and generalisations that are new to the literature.

Lewis Cole

Ryan Cullinan

Argentina

Joaquin Liniado

Belgium

Daniel Thompson

Gauging the diamond: integrable coset models from twistor space

Light-cone gauge-fixed sigma models on <math><msub><mi>AdS</mi><mi>n</mi></msub><mo>×</mo><msup><mi>S</mi><mi>n</mi></msup></math> backgrounds play an important role in the integrability formulation of the <math><mrow><mi>AdS</mi><mo>/</mo><mi>CFT</mi></mrow></math> correspondence. The string spectrum of the sigma model is gauge independent, however the Hamiltonian and scattering matrix of the transverse world sheet fields are not. We study how these change for a large family of inequivalent light-cone gauges, which are interpreted as <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math>, <math><mover><mi>J</mi><mo>˜</mo></mover><msub><mi>T</mi><mi>τ</mi></msub></math>, <math><mi>J</mi><msub><mi>T</mi><mi>σ</mi></msub></math>, and <math><msup><mi>J</mi><mi>τ</mi></msup></math> deformations. We investigate the moduli space of inequivalent light-cone gauges and, specializing to <math><msub><mi>AdS</mi><mn>5</mn></msub><mo>×</mo><msup><mi>S</mi><mn>5</mn></msup></math>, compute the different light-cone gauge symmetry algebras, well known to be <math><mrow><mi>psu</mi><mo>(</mo><mn>2</mn><mo>|</mo><mn>2</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>⊕</mo><mn>2</mn></mrow></msup><mo>⊕</mo><mi>u</mi><mo>(</mo><mn>1</mn><msup><mrow><mo>)</mo></mrow><mrow><mo>⊕</mo><mn>2</mn></mrow></msup></mrow></math> for the standard gauge-fixing. Many integrable deformations require a nonstandard light-cone gauge, hence our classification and analysis of inequivalent gauges will be important for analyzing such models.

Spain

Riccardo Borsato

Sibylle Driezen

Ana L. Retore

Fiona K. Seibold

Inequivalent light-cone gauge-fixings of strings on <math><msub><mi>AdS</mi><mi>n</mi></msub><mo>×</mo><msup><mi>S</mi><mi>n</mi></msup></math> backgrounds

With the aim of investigating the existence of an integrable elliptic deformation of strings on AdS3 × S3 × T4, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on AdS3 × S3 in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden U(1) symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed AdS3 × S3 × T4 light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions.

Ana Retore

Elliptic deformations of the AdS3 × S3 × T4 string

Integrable string sigma models on AdS3 backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-η and bi-λ deformations of two classes of ℤ 4 permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS3 backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-λ deformation.

France

Nat Levine

Bi-η and bi-λ deformations of ℤ 4 permutation supercosets

We construct a family of type IIB string backgrounds that are deformations of AdS3 × S3 × T4 with a “squashed” AdS3 × S3 metric supported by a combination of NSNS and RR fluxes. They have global SU(1, 1) × SU(2) symmetry, regular curvature, constant dilaton and preserve 8 supercharges. Upon compactification to 4 dimensions they reduce to   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supersymmetric AdS2 × S2 solutions with electric and magnetic Maxwell fluxes. These type IIB supergravity solutions can be found from the undeformed AdS3 × S3 × T4 background by a combination of T-dualities and S-duality. In contrast to T-duality, S-duality transformations of a type IIB supergravity background do not generally preserve the classical integrability of the corresponding Green-Schwarz superstring sigma model. Nevertheless, we show that integrability is preserved in the present case. Indeed, we find that these backgrounds can be obtained, up to T-dualities, from an integrable inhomogeneous Yang-Baxter deformation (with unimodular Drinfel’d-Jimbo R-matrix) of the original AdS3 × S3 supercoset model.

Arkady Tseytlin

Integrable supersymmetric deformations of AdS3 × S3 × T4

We study the dual description of the η-deformed OSP(N|2m) sigma model in the asymptotically free regime (N &gt; 2m + 2). Compared to the case of classical Lie groups, for supergroups there are inequivalent η-deformations corresponding to different choices of simple roots. For a class of such deformations we propose the system of screening charges depending on a continuous parameter b, which defines the η-deformed OSP(N|2m) sigma model in the limit b → ∞ and a certain Toda QFT as b → 0. In the sigma model regime we show that the leading UV asymptotic of the η-deformed model coincides with a perturbed Gaussian theory. In the perturbative regime b → 0 we show that the tree-level two-particle scattering matrix matches the expansion of the trigonometric OSP(N|2m) S-matrix.

Russia

Mikhail Alfimov

Boris Feigin

Alexey Litvinov

Dual description of η-deformed OSP sigma models

We consider several classes of σ-models (on groups and symmetric spaces, η-models, ⋋-models) with local couplings that may depend on the 2d coordinates, e.g. on time τ . We observe that (i) starting with a classically integrable 2d σ-model, (ii) formally promoting its couplings h  α  to functions h  α (τ ) of 2d time, and (iii) demanding that the resulting time-dependent model also admits a Lax connection implies that h  α (τ ) must solve the 1-loop RG equations of the original theory with τ interpreted as RG time. This provides a novel example of an ‘integrability-RG flow’ connection. The existence of a Lax connection suggests that these time-dependent σ-models may themselves be understood as integrable. We investigate this question by studying the possibility of constructing non-local and local conserved charges. Such σ-models with D-dimensional target space and time-dependent couplings subject to the RG flow naturally appear in string theory upon fixing the light-cone gauge in a (D + 2)-dimensional conformal σ-model with a metric admitting a covariantly constant null Killing vector and a dilaton linear in the null coordinate.

Sigma models with local couplings: a new integrability-RG flow connection

We extend and complete our analysis arXiv:1608.02380 and study the induced world volume metrics and Hawking temperatures of all type IIB rotating probe Dp-branes, dual to the temperature of different flavors at finite R-charge, in the Ben Ami–Kuperstein–Sonnenschein holographic models including the effects of spontaneous conformal and chiral flavor symmetry breakdown. The model embeds type IIB probe flavor Dp-branes into the Klebanov-Witten gravity dual of conformal gauge theory, with the embedding parameter, given by the minimal radial extension of the probes, dual to the IR scale of conformal and chiral flavor symmetry breakdown. We show that when the minimal extension is positive definite, the induced world volume metrics of type IIB rotating probe branes admit thermal horizons and Hawking temperatures despite the absence of black holes in the bulk subject to the world volume and topology of the nontrivial internal cycle wrapped by the probe. We also derive the energy–stress tensor of the thermal probes and study their backreaction and energy dissipation. We show that at the IR scale the backreaction is nonnegligible and find the energy can flow from the probes to the bulk, dual to the energy dissipation from the flavor sectors into the gauge theory.