QCD_{1+1} with Static Quarks as Supersymmetric Quantum Mechanics

TL;DR

This paper analyzes a solvable model of two static quarks interacting with a Yang-Mills field on a circle, revealing supersymmetry at zero separation and its breaking at finite separation, explaining spectral properties.

Contribution

It provides a detailed reexamination of a model showing how supersymmetry emerges and breaks in a gauge theory with static quarks, linking geometry to spectral features.

Findings

Supersymmetry appears when quarks are at the same point.

Supersymmetry is explicitly broken at finite separation.

The spectral and state vector structure is explained by geometric considerations.

Abstract

We reexamine the solvable model problem of two static, fundamental quarks interacting with a SU(2) Yang-Mills field on a spatial circle, introduced by Engelhardt and Schreiber. If the quarks are at the same point, the model exhibits a quantum mechanical supersymmetry. At finite separation, the supersymmetry is explicitly broken in a way which naturally explains the geometrical nature of spectrum and state vectors of this system.