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

TL;DR

This paper constructs the gravity dual of a deformed ABJM theory as a Yang-Baxter deformation of the $AdS_4\times\mathbb{CP}^3$ superstring, illustrating the link between Abelian $r$-matrices and TsT transformations.

Contribution

It introduces a supercoset construction of $\mathbb{CP}^3$ to realize the gravity dual via Yang-Baxter deformation, highlighting the connection with TsT transformations.

Findings

Constructed the gravity dual using Abelian $r$-matrix satisfying CYBE.

Established the relation between Abelian $r$-matrices and TsT transformations.

Provided a supercoset approach to $\mathbb{CP}^3$ deformation.

Abstract

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.