An improved AFS phase for AdS3 string integrability

TL;DR

This paper proposes modifications to the classical dressing phase in AdS3 string integrability, aligning it with perturbative results, crossing symmetry, and semiclassical limits, improving upon previous models.

Contribution

It introduces a new form of the dressing phase for AdS3 strings, starting with a Q_1 Q_2 term, differing from the AdS5 AFS phase, and validates it against multiple theoretical checks.

Findings

Modified phase matches perturbative calculations

Ensures crossing symmetry compliance

Aligns with semiclassical Bethe equations

Abstract

We propose a number of modifications to the classical term in the dressing phase for integrable strings in AdS3 x S3 x S3 x S1, and check these against existing perturbative calculations, crossing symmetry, and the semiclassical limit of the Bethe equations. The principal change is that the phase for different masses should start with a term Q_1 Q_2, like the one-loop AdS3 dressing phase, rather than Q_2 Q_3 as for the original AdS5 AFS phase.