Quantum integrability of the Alday-Arutyunov-Frolov model

TL;DR

This paper demonstrates the quantum integrability of the Alday-Arutyunov-Frolov model by analyzing three-particle scattering and establishing necessary conditions for integrability, correcting previous oversights.

Contribution

It provides the first detailed calculation of the three-particle S-matrix at one loop for the AAF model and identifies key constraints ensuring its quantum integrability.

Findings

Three-particle S-matrix is factorizable at first non-trivial order.

A necessary constraint for quantum integrability is derived.

Quantum integrability of the AAF model is confirmed under this constraint.

Abstract

We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF) model by calculating the three-particle scattering amplitude at the first non-trivial order and showing that the S-matrix is factorizable at this order. We consider a more general fermionic model and find a necessary constraint to ensure its integrability at quantum level. We then show that the quantum integrability of the AAF model follows from this constraint. In the process, we also correct some missed points in earlier works.