Yang-Baxter deformations of the $AdS_4\times\mathbb{CP}^3$ superstring sigma model

Understand

The gravity dual of $\beta$-deformed ABJM theory can be obtained by a TsT transformation of $AdS_4\times\mathbb{CP}^3$.

• 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.