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.

35 pages

References in corpus (31)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• 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
• 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
• Spacetimes for λ-deformations
• 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
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• Yangian symmetry in deformed WZNW models on squashed spheres
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• 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 Quantum Deformed Mirror TBA I
• On reduced models for superstrings on AdS_n x S^n
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• 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 $(Ad{S}_3\times S^3{)}_{\varkappa }$
• The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Warped anti-de Sitter spaces from brane intersections in type II string theory
• 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
• Minimal surfaces in $q$-deformed AdS${}_5\times$S${}^5$ with Poincare coordinates

Cited by in corpus (26)

• Abelian Yang-Baxter Deformations and TsT transformations
• Yang-Baxter sigma models based on the CYBE
• Integrable Deformations of Sigma Models
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• Double Wick rotating Green-Schwarz strings
• 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
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Generalized $\lambda$-deformations of AdS_p x S^p
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Spiky strings in $\varkappa$-deformed $AdS$
• On circular strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Resurgence in the Bi-Yang-Baxter Model
• Integrable deformations of AdS/CFT
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• 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
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• Bethe Ansatz for Quantum-Deformed Strings
• 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