Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)

TL;DR

This work analyzes worldsheet one-loop corrections in Type IIA string theory on $AdS_3\times S^3\times M^4$, focusing on the regulator-induced ambiguities in the dispersion relation fixed by integrability. Using an implicit regularization scheme that treats all fields equally, it shows that worldsheet supersymmetry selects the consistent regularization (WS), yielding a nonzero one-loop correction, while a regulator that distinguishes heavy modes (AC) breaks SUSY and clashes with integrability. The study then verifies the one-loop dressing phase by explicit $2\to 2$ scattering computations in the full near-BMN string, confirming the modified BOSST phase once Kronecker-delta terms are included, with the strong coupling scale set by $h=2g$. The results bolster the compatibility of integrability-based phase structures with explicit worldsheet calculations and motivate extensions to other backgrounds and interpolation schemes between endpoints of the moduli.

Abstract

In this note we study worldsheet two- and four-point functions at the one-loop level for the type IIA superstring in AdS(3) x S(3) x M(4) . We first address the regularization ambiguity that appears in the dispersion relation derived from integrability. We demonstrate that only the regulator treating all fields equally respects worldsheet supersymmetry. This is done in an implicit regularization scheme where all divergent terms are collected into master tadpole-type integrals. We then investigate one-loop two-body scattering on the string worldsheet and verify that a recent proposal for the dressing phase reproduces explicit worldsheet computations. All calculations are done in a near-BMN like expansion of the Green-Schwarz superstring equipped with quartic fermions.