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 so-called { dual} equation of Sklyanin's. We perform the algebraic Bethe ansatz based on Sklyanin's recipe, 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 provide conjectures for the exact formulas for any number of quantum particles and magnonic excitations.
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Bielli et al. (2024) studied this question.
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