All Jordanian deformations of the $AdS_5 \times S^5$ superstring

Abstract

We explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on \mathfrak{psu}(2,2|4)𝔭𝔰𝔲(2,2|4), corresponding to Jordanian Yang-Baxter deformations of the AdS_5\times S^5AdS5 × S5 superstring. Such deformations preserve the classical integrability of the underlying sigma-model and thus are a subclass of all possible integrable deformations. The deformations that we consider are divided into two families, unimodular and non-unimodular ones. The former ensure that the deformed backgrounds are still solutions of the type IIB supergravity equations. For the simplest unimodular solutions, we find that the corresponding backgrounds preserve a number N < 32 of supercharges that can be N=12,8,6,4,0.