Generalized type IIB supergravity equations and non-Abelian classical r-matrices

Abstract

We study Yang-Baxter deformations of the $Ad{S}_5\times S^5$ superstring with non-Abelian classical $r$-matrices which satisfy the homogeneous classical Yang-Baxter equation (CYBE). By performing a supercoset construction, we can get deformed $Ad{S}_5\times S^5$ backgrounds. While this is a new area of research, the current understanding is that Abelian classical $r$-matrices give rise to solutions of type IIB supergravity, while non-Abelian classical $r$-matrices lead to solutions of the generalized supergravity equations. We examine here some examples of non-Abelian classical r-matrices and derive the associated backgrounds explicitly. All of the resulting backgrounds satisfy the generalized equations. For some of them, we derive "T-dualized" backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type IIB supergravity equations. Remarkably, some of the "T-dualized" backgrounds are locally identical to undeformed $Ad{S}_5\times S^5$ after an appropriate coordinate transformation, but this seems not to be generally the case.

typos corrected

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• Deformations of the Almheiri-Polchinski model
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• Embedding the modified CYBE in Supergravity
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• $O(d,d)$ transformations preserve classical integrability
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• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
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• Generalized Supergravity Equations for the WZW Model
• Yang-Baxter deformations of the OSP(1|2) WZW model
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations