The AdS3 × S3 × S3 × S1 Hernández–López phases: a semiclassical derivation

This note calculates the Hernández–López phases for strings in AdS3 × S3 × S3 × S1 by semiclassical methods using the d(2, 1; α)2 algebraic curve. By working at general α we include modes absent from previous semiclassical calculations of this phase in AdS3 × S3 × T4, and in particular can study the scattering of particles of different mass. By carefully re-deriving the semiclassical formula we clarify some issues of antisymmetrization, cutoffs and surface terms which could safely be ignored in AdS5 × S5, and some issues about the terms c1,s which were absent there. As a result we see agreement with the recently calculated all-loop dressing phase in the AdS3 × S3 × T4 case, and exactly 1/2 this in the general case AdS3 × S3 × S3 × S1, for any α and any (light) polarizations. (paper)