The Circular, Elliptic Three Spin String from the SU(3) Spin Chain

TL;DR

This paper connects a specific three-spin string solution in AdS_5 x S^5 to the integrable SU(3) spin chain, deriving the string from the spin chain sigma model and identifying the Bethe root configuration.

Contribution

It provides a complete description of the three-spin string in terms of the SU(3) spin chain, including a direct derivation and Bethe root configuration analysis.

Findings

Recovered the string solution from the spin chain sigma model

Identified the Bethe root configuration in a new parameter space region

Enhanced the understanding of integrable structures in AdS/CFT

Abstract

We complete the description of the circular, elliptic three spin string on AdS_5 x S^5 having three large angular momenta (J_1,J_2,J_3) on S^5 in the language of the integrable SU(3) spin chain. First, we recover the string solution directly from the spin chain sigma model and secondly, we identify the appropriate Bethe root configuration in the so far unexplored region of parameter space.