Bosonic $\eta$-deformed $Ad{S}_4\times {\mathbb{CP}}^3$ Background

Abstract

We build the bosonic $\eta$-deformed $Ad{S}_4\times {\mathbb{CP}}^3$ 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.

13 pages, added comments in sections 1, 4 and 5; added references [25,26,27], deleted comments on $Ad{S}_4\times S^7$