Lax Pair for Strings in Lunin-Maldacena Background
Abstract
Recently Lunin and Maldacena used an SL(3,R) transformation of the AdS_5 x S^5 background to generate a supergravity solution dual to a so-called beta-deformation of N = 4 super Yang-Mills theory. We use a T-duality-shift-T-duality (TsT) transformation to obtain the beta-deformed background for real beta, and show that solutions of string theory equations of motion in this background are in one-to-one correspondence with those in AdS_5 x S^5 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 beta-deformed background. We also perform a chain of three consecutive TsT transformations to generate a three-parameter deformation of AdS_5 x S^5. The three-parameter background is dual to a nonsupersymmetric marginal deformation of N=4 SYM. Finally, we combine the TsT transformations with SL(2,R) ones to obtain a 6+2 parameter deformation of AdS_5 x S^5.
Keywords
Cite
@article{arxiv.hep-th/0503201,
title = {Lax Pair for Strings in Lunin-Maldacena Background},
author = {Sergey Frolov},
journal= {arXiv preprint arXiv:hep-th/0503201},
year = {2009}
}
Comments
28 pages, v2: a discussion of a 4+2 parameter solution added in section 5; new Appendix B with a 6+2 parameter deformation of AdS_5 x S^5; typos corrected, references added, v3: typos corrected