Magnons, Classical Strings and beta-Deformations

TL;DR

This paper constructs a classical string solution in a beta-deformed background, identifying it with a magnon state in the dual gauge theory, and derives its exact dispersion relation.

Contribution

It provides the first explicit classical string solution corresponding to a magnon in the beta-deformed AdS/CFT setup, extending the integrability framework.

Findings

Derived an exact dispersion relation for the magnon.

Constructed a classical string solution with two angular momenta.

Linked the string solution to a magnon in the spin chain.

Abstract

Motivated by the recent work of Hofman and Maldacena we construct a classical string solution on the beta-deformed AdS_5 \times \tilde{S}^5 background. This string solution is identified with a magnon state of the integrable spin chain description of the N=1 supersymmetric beta-deformed gauge theory. The string solution carries two angular momenta, an infinite J_1 and a finite J_2 which classically can take arbitrary values. It corresponds to the magnon of charge J_2 propagating on an infinite spin chain. We derive an exact dispersion relation for this magnon from string theory.