Transfer matrices for AdS3/CFT2

TL;DR

<3-5 sentence high-level summary>: The paper develops an algebraic Bethe ansatz for the worldsheet theory of the $AdS_3\times S^3\times T^4$ superstring, deriving comprehensive transfer matrices for both the string and mirror models and for their bound states. It carefully handles the model’s multiple fundamental representations (left, right, massless) and shows how to construct the full transfer matrix via a factorised RTT framework, including the role of auxiliary Bethe roots. It then extends the formalism to Abelian twists, deriving how the Bethe equations and transfer matrices are modified by diagonal twists and clarifying the connection to twisted backgrounds and the mirror TBA proposed by Frolov and Sfondrini. The results provide essential building blocks for the mirror TBA analysis and for exploring twisted/deformed AdS3/CFT2 models, with implications for TsT transformations and related backgrounds.

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.