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

The gravity dual of $\beta$-deformed ABJM theory can be obtained by a TsT transformation of $Ad{S}_4\times {\mathbb{C}\mathbb{P}}^3$. We present a supercoset construction of ${\mathbb{C}\mathbb{P}}^3$ 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.