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

In this paper we continue the investigation of aspects of integrability of the type IIA AdS(3) x S-3 x S-3 x S-1 and AdS(3) x S-3 x T-4 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(lambda), to explicit one-loop calculations on the string worldsheet. For AdS(3) x S-3 x S-3 x S-1 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 AdS(4)/CFT3 occur also here.