The complete AdS3 x S3 x T4 worldsheet S matrix

We derive the non-perturbative worldsheet S matrix for fundamental excitations of Type IIB superstring theory on AdS3 × S3 × T4 with Ramond-Ramond flux. To this end, we study the off-shell symmetry algebra of the theory and its representations. We use these to determine the S matrix up to scalar factors and we derive the crossing equations that these scalar factors satisfy. Our treatment automatically includes fundamental massless excitations, removing a long-standing obstacle in using integrability to study the AdS3/CFT2 correspondence. The present paper contains a detailed derivation of results first announced in arXiv:1403.4543.