Lunin-Maldacena deformations with three parameters

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,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 AdS₅ × S⁵, one would expect that our new solutions should correspond to non-supersymmetric marginal deformations of the relevant dual field theories.