gamma_i Deformed Lax Pair for Rotating Strings in the Fast Motion Limit

Abstract

A 3-parameter generalization of the Lunin-Maldacena background has recently been constructed by Frolov. This gamma_i-deformed background is non-supersymmetric. We consider strings in this gamma_i-deformed R \times S^5 background rotating in three orthogonal planes (the 3-spin sector) in a fast motion limit, in which the total angular momentum J is assumed to be large. We show that there exists a consistent transformation which takes the undeformed equations of motion into the gamma_i-deformed equations of motion. This transformation is used to construct a Lax pair for the bosonic part of the gamma_i-deformed theory in the fast motion limit. This implies the integrability of the bosonic part of the gamma_i-deformed string sigma model in the fast motion limit.

arXiv comment21 pages

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• Integrable Spin Chains with U(1)^3 symmetry and generalized Lunin-Maldacena backgrounds
• Semiclassical Strings, Dipole Deformations of N=1 SYM and Decoupling of KK Modes
• Giant Gravitons on Deformed pp-waves
• Probing Universality in the Gravity Duals of N=1 SYM by gamma-deformations
• Pure Spinor Strings in TsT Deformed Background