Microscopic formulation of the S-matrix in AdS/CFT

TL;DR

This paper derives the dressing phase of the S-matrix in AdS/CFT using a microscopic approach based on the Bethe ansatz, providing detailed root distributions and reproducing known phases.

Contribution

It presents a microscopic derivation of the AdS/CFT S-matrix dressing phase within the integrable model framework, detailing Bethe root configurations and their thermodynamic limit.

Findings

Derived the Bethe root distribution for the physical vacuum.

Computed the scattering phase of fundamental excitations.

Reproduced the BHL/BES dressing phase explicitly.

Abstract

We develop the derivation we proposed in hep-th/0703177 of the dressing phase of the S-matrix in the AdS/CFT correspondence in the framework of the underlying bare integrable model. We elaborate the configuration of the Bethe roots describing the physical vacuum, which consists of a long Bethe string stretched along the imaginary axis and stacks distributed along the real axis. We determine the distribution of all Bethe roots in the thermodynamic limit. We then directly compute the scattering phase of the fundamental excitations over the physical vacuum and reproduce the BHL/BES dressing phase.