The complete worldsheet S matrix of superstrings on AdS₃ x S³ x T⁴ with mixed three-form flux

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We determine the off-shell symmetry algebra and representations of Type IIB superstring theory on AdS₃× S³ × T⁴ with mixed R-R and NS-NS three-form flux. We use these to derive the non-perturbative worldsheet S matrix of fundamental excitations of the superstring theory. Our analysis includes both massive and massless modes and shows how turning on mixed three-form flux results in an integrable deformation of the S matrix of the pure R-R theory.