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We obtain the all-loop worldsheet S matrix for fundamental excitations onAdS_3 x S^3 x T^4 by studying the off-shell symmetry algebra of the superspaceaction in lightcone gauge. The massless modes, unaccounted for in earlierworks, are automatically included in our treatment. Their exact dispersionrelation is found to be non-relativistic, of giant-magnon form and theirscattering is naturally well-defined. This opens the way to a completeinvestigation of AdS_3/CFT_2 integrability.

All-loop worldsheet S matrix for AdS_3 x S^3 x T^4