Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence

Abstract

We consider γ-deformations of the AdS_5xS^5 superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real γ-deformations of the AdS_5xS^5 superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.

18 pages, no figure, LaTeX, v2:references and further clarifications added

References in corpus (12)

• On deformations of AdS_n x S^n supercosets
• Quantum Deformations of the One-Dimensional Hubbard Model
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• A Jordanian deformation of AdS space in type IIB supergravity
• Yangian symmetry in deformed WZNW models on squashed spheres
• The Quantum Deformed Mirror TBA I
• Hidden Yangian symmetry in sigma model on squashed sphere
• Twisting the Mirror TBA
• Non-integrability in non-relativistic theories
• Twisted Bethe equations from a twisted S-matrix
• Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality
• Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix

Cited by in corpus (24)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Abelian Yang-Baxter Deformations and TsT transformations
• Yang-Baxter sigma models based on the CYBE
• Integrability of classical strings dual for noncommutative gauge theories
• A Jordanian deformation of AdS space in type IIB supergravity
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Schrödinger geometries arising from Yang-Baxter deformations
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• $T$-folds from Yang-Baxter deformations
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
• Finite-size giant magnons on η-deformed AdS_5 x S^5
• $I$ in generalized supergravity
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Marginal and non-commutative deformations via non-abelian T-duality
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system
• Integrability of the eta-deformed Neumann-Rosochatius model
• Spiky strings in $\varkappa$-deformed $AdS$
• On quantum deformations of $Ad{S}_3\times S^3\times T^4$ and mirror duality
• Deformations of $T^{1,1}$ as Yang-Baxter sigma models
• Tri-vector deformations on compact isometries