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

Orlando, Domenico; Reffert, Susanne; Sakamoto, Jun-ichi; Yoshida, Kentaroh (2016). Generalized type IIB supergravity equations and non-Abelian classical r -matrices. Journal of physics. A - mathematical and theoretical, 49(44), p. 445403. Institute of Physics Publishing IOP 10.1088/1751-8113/49/44/445403

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We study Yang–Baxter deformations of the AdS₅ superstring with non-Abelian classical r-matrices which satisfy the homogeneous classical Yang–Baxter equation. By performing a supercoset construction, we can get deformed AdS₅ x S⁵ 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 AdS₅ x S⁵ after an appropriate coordinate transformation, but this seems not to be generally the case.

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