Lunin-Maldacena Deformations With Three Parameters

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.