Boundary Bethe ansatz in massive $AdS_3$

TL;DR

This paper develops a comprehensive boundary algebraic Bethe Ansatz for massive representations in the integrable $AdS_3$ system, extending previous work on massless cases and exploring various boundary conditions and polarizations.

Contribution

It provides the first detailed analysis of boundary Bethe Ansatz for massive $AdS_3$ representations, including all polarization and boundary type configurations.

Findings

Derived auxiliary Bethe equations for all boundary and polarization cases

Revealed subtle differences in the Bethe Ansatz procedure based on boundary choices

Extended the integrable $AdS_3$ framework to include massive boundary conditions

Abstract

In this paper we perform the boundary algebraic Bethe Ansatz for massive representations of the $AdS_3 \times S^3 \times T^4$ integrable system. This is a companion analysis to our study of massless representations \cite{Bielli:2024bve}. Our treatment is comprehensive of all possible assortments of tensor-factor polarisations which build the physical representations in the spectrum, and includes different choices of auxiliary spaces, revealing subtle differences in the procedure. We survey both singlet and vector boundaries, obtaining the auxiliary Bethe equations in very general form for all cases.