Integrable deformations of the AdS${}_5\times$S${}^5$ superstring and the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence --

Abstract

Based on the formulation of Yang-Baxter sigma models developed by Klimcik and Delduc-Magro-Vicedo, we explain that various deformations of type IIB superstring on AdS${}_5\times$S${}^5$ can be characterized by classical $r$-matrices satisfying the classical Yang-Baxter equation (CYBE). The relation may be referred to as `the gravity/CYBE correspondence.' We present non-trivial examples of the correspondence including Lunin-Maldacena backgrounds for $\beta$-deformations of the $\mathcal{N}=4$ super Yang-Mills theory and the gravity duals for non-commutative gauge theories. We also discuss non-integrable backgrounds such as AdS${}_5\times T^{1,1}$ as a generalization.

17 pages; Submitted to the proceedings of `The XXIInd International Conference on Integrable Systems and Quantum Symmetries (ISQS-22),' Prague, June 23-29, 2014; Based on the talk presented by T.M

References in corpus (3)

• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Yangian symmetry in deformed WZNW models on squashed spheres
• Integrable twists in AdS/CFT

Cited by in corpus (7)

• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Abelian Yang-Baxter Deformations and TsT transformations
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Schrödinger geometries arising from Yang-Baxter deformations
• $T$-folds from Yang-Baxter deformations
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries