Lax Pair for Strings in Lunin-Maldacena Background

Recently Lunin and Maldacena used an SL(3, R) transformation of theAdS5×S background to generate a supergravity solution dual to a so-called β-deformation of N = 4 super Yang-Mills theory. We use a T-duality-shift-T-duality (TsT) transformation to obtain the β-deformed background for real β ≡ γ, and show that solutions of string theory equations of motion in this background are in one-to-one correspondence with those in AdS5×S with twisted boundary conditions imposed on the U(1) isometry fields. We then apply the TsT transformation to derive a local and periodic Lax pair for the bosonic part of string theory in the γ-deformed background. We also perform a chain of three consecutive TsT transformations to generate a three-parameter deformation of AdS5 × S5. The three-parameter background is dual to a nonsupersymmetric marginal deformation of N = 4 SYM. Also at Steklov Mathematical Institute, Moscow. [email protected]