Supersymmetric quantum mechanics of the flux tube

TL;DR

This paper extends the operator product expansion approach to scattering amplitudes in supersymmetric gauge theory by analyzing a flux tube system with both fermionic and bosonic excitations, demonstrating factorization of multiparticle transitions.

Contribution

It introduces a supersymmetric sl(2|1) magnet model to analyze flux tube excitations, generalizing previous bosonic-only models and proving the factorization of multiparticle transitions.

Findings

Eigenfunctions for multiparticle system derived using R-matrix approach

Factorization of pentagon transitions proven at leading order

Extension from bosonic to supersymmetric flux tube excitations

Abstract

The Operator Product Expansion approach to scattering amplitudes in maximally supersymmetric gauge theory operates in terms of pentagon transitions for excitations propagating on a color flux tube. These obey a set of axioms which allow one to determine them to all orders in 't Hooft coupling and confront against explicit calculations. One of the simplifying features of the formalism is the factorizability of multiparticle transitions in terms of single-particle ones. In this paper we extend an earlier consideration of a sector populated by one kind of excitations to the case of a system with fermionic as well as bosonic degrees of freedom to address the origin of the factorization. While the purely bosonic case was analyzed within an integrable noncompact open-spin chain model, the current case is solved in the framework of a supersymmetric sl(2|1) magnet. We find the eigenfunctions for the multiparticle system making use of the R-matrix approach. Constructing resulting pentagon transitions, we prove their factorized form. The discussion corresponds to leading order of perturbation theory.