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

TL;DR

This paper constructs a Lax pair for the bosonic sector of gamma_i-deformed rotating strings in the fast motion limit, demonstrating integrability in a non-supersymmetric background derived from a 3-parameter deformation.

Contribution

It introduces a transformation linking undeformed and gamma_i-deformed equations of motion, enabling the construction of a Lax pair and proving integrability in the fast motion limit.

Findings

Existence of a consistent transformation between undeformed and deformed equations

Construction of a Lax pair for the gamma_i-deformed background

Evidence of integrability in the bosonic sector 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.