All-loop Bethe ansatz equations for AdS3/CFT2

TL;DR

This paper introduces a new set of all-loop Bethe equations for the AdS3/CFT2 integrable system, highlighting differences from previous models and the role of scalar factors in the dressing phases.

Contribution

It proposes a novel formulation of Bethe equations for AdS3/CFT2, incorporating new scalar factors and grading choices, and analyzes their properties and semiclassical limits.

Findings

New Bethe equations differ from previous models

Scalar factors must differ from known phases

Semiclassical limit involves generalized Arutyunov-Frolov-Staudacher phase

Abstract

Using the S-matrix for the d(2,1;alpha)^2 symmetric spin-chain of AdS3/CFT2, we propose a new set of all-loop Bethe equations for the system. These equations differ from the ones previously found in the literature by the choice of relative grading between the two copies of the d(2,1;alpha) superalgebra, and involve four undetermined scalar factors that play the role of dressing phases. Imposing crossing symmetry and comparing with the near-BMN form of the S-matrix found in the literature, we find several novel features. In particular, the scalar factors must differ from the Beisert-Eden-Staudacher phase, and should couple nodes of different masses to each other. In the semiclassical limit the phases are given by a suitable generalization of Arutyunov-Frolov-Staudacher phase.