Bosonic η-deformed AdS4 × $$ \mathbb{CP} $$3 background

Abstract

We build the bosonic η-deformed AdS4 × $$ \mathbbm{CP} $$ 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.

Bosonic $η$-deformations of Non-integrable Backgrounds

“…In this paper we have obtained the bosonic η-deformed W 2,4 × T 1,1 and AdS 5 × T 1,1 backgrounds based on a solution of the mCYBE. These results provide new integrable backgrounds in addition to those found in [14,20,22]. In another context, Arutyunov et al [25] showed that it is possible to obtain an integrable T 1,1 background, which has an NSNS B-field.…”

“…The extension of this construction, which is based on a solution of the modified classical Yang-Baxter equation (mCYBE), to a symmetric coset space was given by Delduc et al in [9], and to a semisymmetric coset space, as is the case of strings in AdS 5 × S 5 , in [10,11] 1 , leading to the so-called η-deformed AdS 5 × S 5 background in [12,13]. Recently, the σ-model on the supercoset uosp (2,2|6) so(1,3)⊕u (3) , which describes partially strings in AdS 4 × CP 3 , was considered in [14]. On the other hand, some instances of integrable deformations of the AdS 5 × S 5 and AdS 4 × CP 3 backgrounds were given based on solutions of the classical Yang-Baxter equation (CYBE) in [15][16][17][18][19].…”

Bosonic η-deformations of non-integrable backgrounds

“…This construction, which is based on a solution of the modified classical Yang-Baxter equation (mCYBE), can be extended to symmetric coset spaces [8] and to semi-symmetric coset spaces, as is the case of superstrings in AdS 5 × S 5 [9,10] leading to the so called η-deformed AdS 5 × S 5 background [11,12]. Recently, this kind of deformation was applied to the sigma model on the supercoset uosp (2,2|6) so(1,3)⊕u(3) which partially describes superstrings in AdS 4 ×CP 3 [13]. Besides that, some instances of integrable deformations of the AdS 5 × S 5 and AdS 4 × CP 3 backgrounds were also given based on solutions of the classical Yang-Baxter equation (CYBE) in [14][15][16][17][18].…”