On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring

Abstract

Interesting deformations of AdS_5 x S^5 such as the gravity dual of noncommutative SYM and Schödinger spacetimes have recently been shown to be integrable. We clarify questions regarding the reality and integrability properties of the associated construction based on R matrices that solve the classical Yang-Baxter equation, and present an overview of manifestly real R matrices associated to the various deformations. We also discuss when these R matrices should correspond to TsT transformations, which not all do, and briefly analyze the symmetries preserved by these deformations, for example finding Schrödinger superalgebras that were previously obtained as subalgebras of psu(2,2|4). Our results contain a (singular) generalization of an apparently non-TsT deformation of AdS_5 x S^5, whose status as a string background is an interesting open question.

v2, 16 pages, published version

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Cited by in corpus (34)

• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Abelian Yang-Baxter Deformations and TsT transformations
• Almost abelian twists and AdS/CFT
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• Generalized gravity from modified DFT
• $T$-folds from Yang-Baxter deformations
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• Deformations of the Almheiri-Polchinski model
• Non-abelian tri-vector deformations in d=11 supergravity
• Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system
• Yang-Baxter invariance of the Nappi-Witten model
• Supercoset construction of Yang-Baxter deformed AdS${}_5\times$S${}^5$ backgrounds
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$
• Yang-Baxter deformations of Minkowski spacetime
• Scalar fields on λ-deformed cosets
• Analytical Structure of the Generalized $\lambda -$deformation
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Yang-Baxter deformations of $W_{2,4}\times T^{1,1}$ and the associated T-dual models
• D-brane on Deformed AdS_3 times S^3
• Yang-Baxter deformations of the $Ad{S}_4\times {\mathbb{CP}}^3$ superstring sigma model
• Bubbling geometries for AdS_2 x S^2
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• Integrable Hopf twists, marginal deformations and generalised geometry
• Lax pairs on Yang-Baxter deformed backgrounds
• Asymmetric $\lambda$-deformed cosets