Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase

TL;DR

This paper computes the leading quantum correction to the dressing phase in superstring theory on AdS_3 x S^3 x T^4, revealing differences from the known AdS_5 case and analyzing the dependence on geometric parameters.

Contribution

It introduces the first calculation of the quantum correction to the dressing phase in AdS_3 x S^3 x T^4 and explores its dependence on the geometry and flux parameters.

Findings

The dressing phase differs from the BES phase in AdS_5 x S^5.

Quantum correction vanishes in the T^4 case.

The correction depends on the ratio of sphere radii in S^3 x S^3 x S^1.

Abstract

We study the leading quantum string correction to the dressing phase in the asymptotic Bethe Ansatz system for superstring in AdS_3 x S^3 x T^4 supported by RR flux. We find that the phase should be different from the BES phase appearing in the AdS_5 x S^5 case. We use the simplest example of a rigid circular string with two equal spins in S^3 and also consider the general approach based on the algebraic curve description. We also discuss the case of the AdS_3 x S^3 x S^3 x S^1 theory and find the dependence of the 1-loop correction to the effective string tension function h(\lambda) (expected to enter the magnon dispersion relation) on the parameters alpha related to the ratio of the two 3-sphere radii. This correction vanishes in the AdS_3 x S^3 x T^4 case.