New Dressing Factors for AdS3/CFT2

The worldsheet S matrix of strings on the $AdS_3\times S^3\times T^4$ background is almost entirely fixed by symmetries, up to five functions -- the dressing factors. These must satisfy several consistency conditions, in particular a set of crossing equations. We find that the existing proposal for the dressing factors, while crossing invariant, violates some of these consistency conditions. We put forward a new set of dressing factors and discuss in detail their analytic properties in the string and mirror region, as well as under bound-state fusion.