Bosonic $\eta$-deformed $AdS_4\times\mathbb{CP}^3$ Background

TL;DR

This paper constructs a bosonic $ a$-deformed $AdS_4 imes C P^3$ background using an $r$-matrix satisfying the modified classical Yang-Baxter equation, revealing a gravity dual of noncommutative ABJM theory in a special limit.

Contribution

It introduces a new $ a$-deformed background for $AdS_4 imes C P^3$ based on an $r$-matrix satisfying the modified classical Yang-Baxter equation, linking to noncommutative ABJM theory.

Findings

Constructed the $ a$-deformed background using an $r$-matrix.

Identified the background as a gravity dual of noncommutative ABJM theory.

Special limit connects to known noncommutative gauge theories.

Abstract

We build the bosonic $\eta$-deformed $AdS_4\times\mathbb{CP}^3$ background generated by an $r$-matrix that satisfies the modified classical Yang-Baxter equation. In a special limit we find that it is the gravity dual of the noncommutative ABJM theory.