Classical integrability and quantum aspects of the AdS3 × S3 × S3 × S1 superstring

In this paper we continue the investigation of aspects of integrability of the type IIA AdS3 × S3 × S3 × S1 and AdS3 × S3 × T4 superstrings. By constructing a one parameter family of flat connections we prove that the Green-Schwarz string is classically integrable, at least to quadratic order in fermions, without fixing the kappa-symmetry. We then compare the quantum dispersion relation, fixed by integrability up to an unknown interpolating function h(λ), to explicit one-loop calculations on the string worldsheet. For AdS3 × S3 × S3 × S1 the spectrum contains heavy, as well as light and massless modes, and we find that the one-loop contribution differs depending on how we treat these modes showing that similar regularization ambiguities as appeared in AdS4/CFT3 occur also here.