The AdS3xS3xS3xS1 worldsheet S matrix

We investigate type IIB strings on AdS3 S3S3 S1 with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux. By suitably gauge-fixing the closed string Green-Schwarz action of this theory, we derive the off-shell symmetry algebra and its representations. We use these to determine the non-perturbative worldsheet S matrix of fundamental excitations in the theory. The analysis involves both massive and massless modes in complete generality. The S matrix we find involves a number of phase factors, which in turn satisfy crossing equations that we also determine. We comment on the nature of the heaviest modes of the theory, but leave their identification either as composites or bound-states to a future investigation.