Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring

TL;DR

This paper demonstrates the classical integrability of the AdS(3) x S(3) x S(3) x S(1) superstring and explores quantum corrections, revealing regularization ambiguities in the spectrum analysis.

Contribution

It constructs a family of flat connections proving classical integrability without fixing kappa-symmetry and compares quantum dispersion relations with one-loop calculations.

Findings

Classical integrability established up to quadratic fermions.

Quantum dispersion relation matches one-loop calculations with an unknown interpolating function.

Regularization ambiguities affect the spectrum analysis, similar to AdS(4)/CFT(3).

Abstract

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)/CFT(3) occur also here.