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.

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

References in corpus (12)

• Bethe Ansatz for Quantum Strings
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• Classical/quantum integrability in non-compact sector of AdS/CFT
• The Algebraic Curve of 1-loop Planar N=4 SYM
• SL(2) spin chain and spinning strings on AdS_5xS^5
• Spin chain sigma models with fermions
• Semiclassical Strings on AdS_5 x S^5/Z_M and Operators in Orbifold Field Theories
• Bethe ansatz and fluctuations in SU(3) Yang-Mills operators
• The Circular, Elliptic Three Spin String from the SU(3) Spin Chain

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