Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model

Abstract

We propose that the Yang-Baxter deformation of the symmetric space sigma-model parameterized by an r-matrix solving the homogeneous (classical) Yang-Baxter equation is equivalent to the non-abelian dual of the undeformed model with respect to a subgroup determined by the structure of the r-matrix. We explicitly demonstrate this on numerous examples in the case of the AdS_5 sigma-model. The same should also be true for the full AdS_5 x S^5 supercoset model, providing an explanation for and generalizing several recent observations relating homogeneous Yang-Baxter deformations based on non-abelian r-matrices to the undeformed AdS_5 x S^5 model by a combination of T-dualities and non-linear coordinate redefinitions. This also includes the special case of deformations based on abelian r-matrices, which correspond to TsT transformations: they are equivalent to non-abelian duals of the original model with respect to a central extension of abelian subalgebras.