Yang-Baxter deformations of the $Ad{S}_4\times {\mathbb{CP}}^3$ superstring sigma model

Abstract

The gravity dual of $\beta$-deformed ABJM theory can be obtained by a TsT transformation of $Ad{S}_4\times {\mathbb{CP}}^3$. We present a supercoset construction of ${\mathbb{CP}}^3$ to obtain this gravity dual theory as a Yang-Baxter deformation. This is done by selecting a convenient combination of Cartan generators in order to get an Abelian $r$-matrix satisfying the classical Yang-Baxter equation. Our results provide another illustration of the relation between Abelian $r$-matrices and TsT transformations.

15 pages; v2: references added; v3: more references added, minor corrections, published version