Classical limit of Quantum Sigma-Models from Bethe Ansatz

TL;DR

This paper demonstrates how classical solutions of integrable sigma models can be derived from their quantum Bethe ansatz equations, providing a systematic justification and applying it to the AdS/CFT correspondence.

Contribution

It introduces a new systematic method to derive classical finite gap solutions from quantum Bethe ansatz equations, clarifying the role of Virasoro constraints.

Findings

Reproduced classical finite gap solutions from quantum Bethe ansatz.

Applied method to AdS/CFT, reproducing the asymptotic string Bethe ansatz.

Clarified the role of Virasoro constraints in the integrability framework.

Abstract

In these proceedings we review the results of [1-3]. We show on the example of the SU(2) chiral-field how to reproduce the classical finite gap solutions for a large class of integrable sigma models from their exact quantum solutions. These solutions are usually formulated as Bethe ansatz equations for physical particles on a circle, with the interaction given by the factorized S-matrix conjectured from Zamolodchikovs' bootstrap procedure. Our method opens a new systematic way to justify this procedure. As an application of our method to the integrability in AdS/CFT correspondence, we reproduce the asymptotic string Bethe ansatz conjectured eartlier in the S3 x R sector of the Green-Schwarz-Metsaev-Tseytlin superstring. The role of the Virasoro constraints in this setup is clarified.