Lunin-Maldacena Deformations With Three Parameters

TL;DR

This paper analyzes the symmetries used to generate gravity duals of beta-deformations in field theories, introduces a new three-parameter deformation of certain manifolds, and clarifies the mathematical structure behind these deformations.

Contribution

It identifies the O(2,2,R) matrix acting on background fields, simplifying calculations and revealing features of deformed backgrounds, and introduces a novel three-parameter deformation of Sasaki-Einstein manifolds.

Findings

Simplified the calculation of deformed backgrounds using O(2,2,R) symmetry.

Discovered a new three-parameter deformation of T^{1,1} and Y^{p,q} manifolds.

Suggested these deformations correspond to non-supersymmetric marginal deformations.

Abstract

We examine the solution generating symmetries by which Lunin and Maldacena have generated the gravity duals of beta-deformations of certain field theories. We identify the O(2,2,R) 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 \times S^5, one would expect that our new solutions should correspond to non-supersymmetric marginal deformations of the relevant dual field theories.