Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings

Abstract

We construct a two-parameter deformation of the Metsaev-Tseytlin action for supercosets with isometry group of the form G x G. The resulting action is classically integrable and is Poisson-Lie symmetric suggesting that the symmetry of the model is q-deformed, U_q_L(G) x U_q_R(G). Focusing on the cases relevant for strings moving in AdS_3 x S^3 x T^4 and AdS_3 x S^3 x S^3 x S^1, we analyze the corresponding deformations of the AdS_3 and S^3 metrics. We also construct a two-parameter $q$-deformation of the u(1) + psu(1|1)^2 x u(1) x R^3-invariant R-matrix and closure condition, which underlie the light-cone gauge S-matrix and dispersion relation of the aforementioned string theories. With the appropriate identification of parameters, the near-BMN limit of the dispersion relation is shown to agree with that found from the deformed supercoset sigma model.

arXiv comment35 pages

References in corpus (70)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Type IIB superstring action in AdS_5 x S^5 background
• Transcendentality and Crossing
• The su(2|2) Dynamic S-Matrix
• On integrability of the Yang-Baxter $\si$-model
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• An integrable deformation of the AdS_5 x S^5 superstring action
• 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
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Integrability and the AdS(3)/CFT(2) correspondence
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• On deformations of AdS_n x S^n supercosets
• An Integrable Deformation of the AdS5 x S5 Superstring
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Integrability of the bi-Yang-Baxter sigma-model
• Quantum Deformations of the One-Dimensional Hubbard Model
• On the Singularities of the Magnon S-matrix
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Integrable Deformations of Strings on Symmetric Spaces
• The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
• 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
• Spacetimes for λ-deformations
• A dynamic su(1|1)^2 S-matrix for AdS3/CFT2
• Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
• On the Hopf algebra structure of the AdS/CFT S-matrix
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• Dressing phases of AdS3/CFT2
• Integrable double deformation of the principal chiral model
• Supergravity backgrounds for deformations of AdS_n x S^n supercoset string models
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• String Theory on AdS_3 x S^3 x S^3 x S^1
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Yangian symmetry in deformed WZNW models on squashed spheres
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• The magnon kinematics of the AdS/CFT correspondence
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• 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
• The GS Type IIB Superstring Action on AdS(3) X S(3) X T(4)
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Superisometries and integrability of superstrings
• The Quantum Deformed Mirror TBA II
• A deformation of quantum affine algebra in squashed WZNW models
• Finite Size Giant Magnon
• Deformed Neumann model from spinning strings on (AdS_5 x S^5)_η
• A Quantum Affine Algebra for the Deformed Hubbard Chain
• Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality
• Finite-size giant magnons on η-deformed AdS_5 x S^5
• On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• Warped anti-de Sitter spaces from brane intersections in type II string theory
• 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
• Giant Magnon on Deformed AdS(3)xS(3)
• Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• The Bound State S-matrix of the Deformed Hubbard Chain
• Integrable Superstrings on the Squashed Three-sphere
• Minimal surfaces in $q$-deformed AdS${}_5\times$S${}^5$ with Poincare coordinates

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• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Abelian Yang-Baxter Deformations and TsT transformations
• Yang-Baxter sigma models based on the CYBE
• Supergravity backgrounds for deformations of AdS_n x S^n supercoset string models
• Integrable Deformations of Sigma Models
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• 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
• Quantum deformations of the flat space superstring
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Killing(-Yano) Tensors in String Theory
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model
• The Effectiveness of Relativistic Invariance in AdS${}_3$
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Two-parameter integrable deformations of the $Ad{S}_3\times S^3\times T^4$ superstring
• Non-split and split deformations of AdS_5
• Dressing cosets and multi-parametric integrable deformations
• Yangian of AdS3/CFT2 and its deformation
• Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting
• Local charges in involution and hierarchies in integrable sigma-models
• Affine q-deformed symmetry and the classical Yang-Baxter sigma-model
• Generalized $\lambda$-deformations of AdS_p x S^p
• Three-parameter integrable deformation of Z_4 permutation supercosets
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type models
• Spiky strings in $\varkappa$-deformed $AdS$
• On circular strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincaré
• Embedding the modified CYBE in Supergravity
• Complex structure-induced deformations of sigma-models
• Quantum deformations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries in unified $\mathfrak{o}(4;\mathbb{C})$ setting -- Addendum
• Resurgence in the Bi-Yang-Baxter Model
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• $O(d,d)$ transformations preserve classical integrability
• Integrable deformations of AdS/CFT
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• Analytical Structure of the Generalized $\lambda -$deformation
• Scalar fields on λ-deformed cosets
• Multispin magnons on deformed $Ad{S}_3\times S^3$
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• D-brane on Deformed AdS_3 times S^3
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• Quantizations of D=3 Lorentz symmetry
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Boost generator in AdS_3 integrable superstrings for general braiding
• Bubbling geometries for AdS_2 x S^2
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• A study of integrable form factors in massless relativistic AdS_3
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• Some three-point correlation functions in the eta-deformed AdS_5 x S^5
• Generalized quark-antiquark potentials from a $q$-deformed AdS${}_5\times$S${}^5$ background
• Spin chains and classical strings in two parameters $q$-deformed AdS${}_3\times$S${}^3$
• Lax pairs on Yang-Baxter deformed backgrounds
• Bethe Ansatz for Quantum-Deformed Strings
• Double Yang-Baxter deformation of spinning strings
• Asymmetric $\lambda$-deformed cosets
• Norms and scalar products for AdS_3
• Asymptotics in the bi-Yang-Baxter Sigma Model
• Yang-Baxter deformations and string dualities
• Pulsating string solution and stability in two parameter $\chi$-deformed background