The complete one-loop BMN S-matrix in AdS₃×S³×T⁴

We compute the full one-loop 2-particle S-matrix for excitations of the type IIB AdS₃×S³×T⁴ BMN string. The S-matrix is found to respect the expected symmetries and the phases are consistent with the crossing equations. By analyzing how the relevant integrals scale with the IR regulator we show that scattering of massless bosons is trivial at two loops. Based on our results we argue that the additional su(2) S-matrix appearing in the massless sector in the exact solution should trivialize.