On deformations of AdS_n x S^n supercosets

Abstract

We study the deformed AdS_5 x S^5 supercoset model of arXiv:1309.5850 which depends on one parameter kappa and has classical quantum group symmetry. We confirm the conjecture that in the "maximal" deformation limit kappa -> infinity this model is T-dual to "flipped" double Wick rotation of the target space AdS_5 x S^5, i.e. dS_5 x H^5 space supported by an imaginary 5-form flux. In the imaginary deformation limit, kappa -> i, the corresponding target space metric is of a pp-wave type and thus the resulting light-cone gauge S-matrix becomes relativistically invariant. Omitting non-unitary contributions of imaginary WZ terms, we find that this tree-level S-matrix is equivalent to that of the generalized sine-Gordon model representing the Pohlmeyer reduction of the undeformed AdS_5 x S^5 superstring model. We also study in some detail similar deformations of the AdS_3 x S^3 and AdS_2 x S^2 supercosets. The bosonic part of the deformed AdS_3 x S^3 model happens to be equivalent to the symmetric case of the sum of the Fateev integrable deformation of the SL(2) and SU(2) principal chiral models, while in the AdS_2 x S^2 case the role of the Fateev model is played by the 2d "sausage" model. The kappa = i limits are again directly related to the Pohlmeyer reductions of the corresponding AdS_n x S^n supercosets: (2,2) super sine-Gordon model and its complex sine-Gordon analog. We also discuss possible deformations of AdS_3 x S^3 with more than one parameter.

arXiv comment31 pages; v2: 33 pages, comments on unitarity and finiteness added and misprints corrected; v3: minor changes

References in corpus (59)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Review of AdS/CFT Integrability: An Overview
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Penrose limits and maximal supersymmetry
• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Lax Pair for Strings in Lunin-Maldacena Background
• Timelike T-Duality, de Sitter Space, Large $N$ Gauge Theories and Topological Field Theory
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Superstring Theory on AdS_2 x S^2 as a Coset Supermanifold
• Exact Black String Solutions in Three Dimensions
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Integrability and the AdS(3)/CFT(2) correspondence
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• Jordanian deformations of the AdS_5xS^5 superstring
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• On String S-matrix, Bound States and TBA
• Generalized Duality in Curved String-Backgrounds
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Quantum Deformations of the One-Dimensional Hubbard Model
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
• Strings on Semisymmetric Superspaces
• Exact Duality Symmetries in CFT and String Theory
• Green-Schwarz Strings in TsT-transformed backgrounds
• Marginal Deformations of WZNW and Coset Models from O(d,d) Transformation
• Superstrings on AdS_5 x S^5 supertwistor space
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• On T-Duality and Integrability for Strings on AdS Backgrounds
• A Jordanian deformation of AdS space in type IIB supergravity
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Superstrings in AdS(2)xS(2)xT(6)
• Four Dimensional Plane Wave String Solutions with Coset CFT Description
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• Strings on pp-waves and massive two dimensional field theories
• The classical origin of quantum affine algebra in squashed sigma models
• On exact solutions and singularities in string theory
• The integrable harmonic map problem versus Ricci flow
• The Quantum Deformed Mirror TBA I
• On reduced models for superstrings on AdS_n x S^n
• A class of exact pp-wave string models with interacting light-cone gauge actions
• A truly marginal deformation of SL(2,R) in a null direction
• Sine-Gordon-like action for the Superstring in AdS(5) x S(5)
• On a `universal' class of WZW-type conformal models
• The Quantum Deformed Mirror TBA II
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• Duality, Marginal Perturbations and Gauging
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
• Tree-level S-matrix of Pohlmeyer reduced form of AdS_5 x S^5 superstring theory
• A Relativistic Relative of the Magnon S-Matrix
• Yang-Baxter sigma models: Quantum aspects
• Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix
• On integrable models from pp-wave string backgrounds
• Worldsheet Supersymmetry of Pohlmeyer-Reduced AdS_n x S^n Superstrings
• Symplectic Deformations of Integrable Field Theories and AdS/CFT
• Integrability vs Supersymmetry: Poisson Structures of The Pohlmeyer Reduction

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• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
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• An Integrable Deformation of the AdS5 x S5 Superstring
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• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
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• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Supergravity background of lambda-deformed model for AdS2 x S2 supercoset
• Beta Function of k Deformed AdS_5 x S^5 String Theory
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• Poisson-Lie T-duals of the bi-Yang-Baxter models
• Double Wick rotating Green-Schwarz strings
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
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• Quantum deformations of the flat space superstring
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• Puzzles of eta-deformed AdS_5 x S^5
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• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
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• Quantum Inverse Scattering and the Lambda Deformed Principal Chiral Model
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• Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
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• Deformed WZW Models and Hodge Theory -- Part I
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