Supercoset construction of Yang-Baxter deformed AdS${}_5\times$S${}^5$ backgrounds

Abstract

We proceed to study Yang-Baxter deformations of the AdS${}_5\times$S${}^5$ superstring with the classical Yang-Baxter equation. We make a general argument on the supercoset construction and present the master formula to describe the dilaton in terms of classical $r$-matrices. The supercoset construction is explicitly performed for some classical $r$-matrices and the full backgrounds including the Ramond-Ramond (R-R) sector and dilaton are derived. Within the class of abelian $r$-matrices, the perfect agreement is shown for well-known examples including gravity duals of non-commutative gauge theories, $\gamma$-deformations of S${}^5$ and Schrödinger spacetimes. It would be remarkable that the supercoset construction works well, even if the resulting backgrounds are not maximally supersymmetric. In particular, three-parameter $\gamma$-deformations of S${}^5$ and Schrödinger spacetimes do not preserve any supersymmetries. As for non-abelian $r$-matrices, we will focus upon a specific example. The resulting background does not satisfy the equation of motion of the Neveu-Schwarz-Neveu-Schwarz (NS-NS) two-form because the R-R three-form is not closed.

32 pages, v2: typos corrected, presentation improved, v3: further typos corrected, accepted in PTEP, v4: further typos corrected

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• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
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• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• Generalized gravity from modified DFT
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• $T$-folds from Yang-Baxter deformations
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly
• Weyl invariance of string theories in generalized supergravity backgrounds
• Deformations of the Almheiri-Polchinski model
• Integrable strings for AdS/CFT
• Analytical Structure of the Generalized $\lambda -$deformation
• Yang-Baxter deformations of $W_{2,4}\times T^{1,1}$ and the associated T-dual models
• Yang-Baxter deformations of the $Ad{S}_4\times {\mathbb{CP}}^3$ superstring sigma model
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations