From nesting to dressing

TL;DR

This paper reveals that in many relativistic integrable field theories, the scalar factor of the S-matrix can be reconstructed from nested Bethe ansatz kernels, providing a new perspective on the dressing factor in AdS integrability.

Contribution

It proposes a method to derive the scalar factor from nested Bethe equations and applies it to recover the AdS dressing factor.

Findings

Scalar factor expressed as convolution of kernels in nested Bethe ansatz

Proposal successfully applied to several relativistic theories

Reconstruction of AdS dressing factor from nested Bethe equations

Abstract

In integrable field theories the S-matrix is usually a product of a relatively simple matrix and a complicated scalar factor. We make an observation that in many relativistic integrable field theories the scalar factor can be expressed as a convolution of simple kernels appearing in the nested levels of the nested Bethe ansatz. We formulate a proposal, up to some discrete ambiguities, how to reconstruct the scalar factor from the nested Bethe equations and check it for several relativistic integrable field theories. We then apply this proposal to the AdS asymptotic Bethe ansatz and recover the dressing factor in the integral representation of Dorey, Hofman and Maldacena.