Transfer matrices for AdS3/CFT2

TL;DR

This paper develops the algebraic Bethe ansatz for the AdS3/CFT2 superstring worldsheet theory, deriving transfer matrices for particles and bound states, and explores modifications due to Abelian twists, aiding in the study of mirror thermodynamic Bethe ansatz equations.

Contribution

It provides the first detailed derivation of transfer matrices and Bethe equations for the AdS3/CFT2 superstring, including effects of Abelian twists, advancing integrability methods in this context.

Findings

Derived transfer matrices for fundamental particles and bound states.

Showed how Bethe equations are modified by Abelian twists.

Laid groundwork for analyzing twisted and deformed models.

Abstract

We work out the algebraic Bethe ansatz for the worldsheet theory of the $AdS_3\times S^3\times T^4$ superstring, and use it to derive the transfer matrices for fundamental particles and bound states of the string and mirror model. We also show how the Bethe equations and transfer matrices are modified in the presence of an Abelian twist. These will be an important ingredient in the exploration of the mirror thermodynamic Bethe ansatz equations recently proposed by Frolov and Sfondrini, and their generalisation to twisted and deformed models.