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.

arXiv comment17 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 (27)

• The Large N Limit of Superconformal Field Theories and Supergravity
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Review of AdS/CFT Integrability: An Overview
• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Type IIB superstring action in AdS_5 x S^5 background
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• On integrability of the Yang-Baxter $\si$-model
• Large N Limit of Non-Commutative Gauge Theories
• An integrable deformation of the AdS_5 x S^5 superstring action
• Lax Pair for Strings in Lunin-Maldacena Background
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Non-Commutative Yang-Mills and the AdS/CFT Correspondence
• Extended jordanian twists for Lie algebras
• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Superstrings on AdS_5 x S^5 supertwistor space
• Hybrid classical integrability in squashed sigma models
• Yangian symmetry in deformed WZNW models on squashed spheres
• Lunin-Maldacena Deformations With Three Parameters
• A deformation of quantum affine algebra in squashed WZNW models
• Causal structures and holography
• New rational solutions of Yang-Baxter equation and deformed Yangians
• Integrable twists in AdS/CFT
• String Theory in Beta Deformed Spacetimes
• Yang-Baxter sigma models: Quantum aspects
• Melvin Twists of global AdS_5 \times S_5 and their Non-Commutative Field Theory Dual

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