Boundary Bethe ansatz in massless AdS3

TL;DR

This paper develops a boundary algebraic Bethe Ansatz framework for the massless sector of the AdS3 X S3 X T4 integrable model, deriving spectrum formulas and Bethe equations.

Contribution

It introduces the boundary algebraic Bethe Ansatz for the massless sector of AdS3 X S3 X T4, including monodromy, dual equations, and exact spectrum formulas.

Findings

Constructed the boundary algebraic Bethe Ansatz for massless AdS3 X S3 X T4.

Derived the double-row monodromy and dual Sklyanin equations.

Obtained Bethe equations and spectrum formulas for arbitrary particle numbers.

Abstract

We construct the boundary algebraic Bethe Ansatz for the AdS3 X S3 X T4 integrable reflection problem restricted to the massless sector. We derive the double-row monodromy and find the appropriate formulation of the dual equation of Sklyanin's. We perform the algebraic Bethe ansatz and obtain the RTT (more properly the RTRT) relations, from which the spectrum is obtained by repeated action of the B operator on the pseudovacuum. We obtain the Bethe equations by cancelling the unwanted terms, and prove the exact formulae for any number of quantum particles and magnonic excitations.