Lunin-Maldacena deformations with three parameters

Abstract

We examine the solution generating symmetries by which Lunin and Maldacena have generated the gravity duals of β-deformations of certain field theories. We identify the O(2, 2, IR) matrix, which acts on the background matrix E = g + B, where g and B are the metric and the B-field of the undeformed background, respectively. This simplifies the calculations and makes some features of the deformed backgrounds more transparent. We also find a new three-parameter deformation of the Sasaki-Einstein manifolds T 1,1 and Y p,q . Following the recent literature on the three-parameter deformation of AdS 5 × S 5 , one would expect that our new solutions should correspond to non-supersymmetric marginal deformations of the relevant dual field theories.

Lax pairs for deformed Minkowski spacetimes

“…Further remarkably, these deformations may work for non-integrable backgrounds, such as a Sasaki-Einstein manifold T 1,1 [33,34]. TsT transformations of T 1,1 [16,35] are reproduced as Yang-Baxter deformations [36,37]. Thus the connection between gravity solutions and classical r-matrices may deserve to be called the gravity/CYBE correspondence (For a short summary see [38]).…”

Yang-Baxter deformations of Minkowski spacetime

“…The case of AdS 5 × T 1,1 is known to be non-integrable [60]. However, deformations of this background [39,61] can be reproduced as Yang-Baxter deformations [62]. The above relations between gravity solutions and classical r-matrices may be called the gravity/cybe correspondence (for a brief summary, see [63]).…”

Strings on the deformedT1,1: giant magnon and single spike solutions

“…The powerful solution generating technique based on the Lunin-Maldacena construction has been applied to various backgrounds in [30,38]. The deformations in these papers also include the conifold which is certainly of interest for the AdS/CFT correspondence.…”

“…First we will give a short set up of the beta-deformed conifold [30,38]. Next we consider a solitonic ansatz for the giant magnon and single spike classical string solutions and find the explicit form of the solutions.…”

“…Since the beta-deformed T 1,1 is known, we will quote here only its final form referring for instance to [30,38]. The starting point of the deformation procedure is the metric of…”