The Anatomy of Gauge/String Duality in Lunin-Maldacena Background

TL;DR

This paper explores the correspondence between spinning string solutions in the Lunin-Maldacena background and dual gauge theory operators, deriving explicit energy-spin relations and analyzing the effects of deformation on Bethe string configurations.

Contribution

It introduces new elliptic solutions in the deformed SU(2) sector and connects string energies with gauge theory anomalous dimensions, extending previous results.

Findings

Derived explicit string energy formulas in terms of moduli.

Computed one-loop anomalous dimensions for dual operators.

Proposed how Bethe string locations are affected by deformation.

Abstract

We consider the correspondence between the spinning string solutions in Lunin-Maldacena background and the single trace operators in the Leigh-Strassler deformation of N=4 SYM. By imposing an appropriate rotating string ans\"atz on the Landau-Lifshitz reduced sigma model in the deformed SU(2) sector, we find two types of `elliptic' solutions with two spins, which turn out to be the solutions associated with the Neumann-Rosochatius system. We then calculate the string energies as functions of spins, and obtain their explicit forms in terms of a set of moduli parameters. On the deformed spin-chain side, we explicitly compute the one-loop anomalous dimensions of the gauge theory operators dual to each of the two types of spinning string solutions, extending and complementing the results of hep-th/0511164. Moreover, we propose explicit ans\"atze on how the locations of the Bethe strings are affected due to the deformation, with several supports from the string side.