Vasileios Moustakis

In this paper we perform the boundary algebraic Bethe Ansatz for massive representations of the AdS₃ × S³ × T⁴ integrable system. This is a companion analysis to our study of massless representations [26]. 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.

We construct the boundary algebraic Bethe ansatz for the AdS3 × S3 × 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 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.