Interacting Fermion Systems from Two Dimensional QCD

TL;DR

This paper maps two-dimensional U(N) QCD with a Wilson line to a system of N interacting fermions with internal degrees of freedom, providing explicit spectrum and degeneracy calculations.

Contribution

It establishes an exact equivalence between 2D U(N) QCD with a Wilson line and a fermionic system with generalized Sutherland interactions, including spectrum analysis.

Findings

Derived the spectrum and degeneracies of the fermionic system

Established the equivalence between 2D QCD and interacting fermions

Explicitly evaluated Wilson line expectation values

Abstract

We consider two dimensional U(N) QCD on the cylinder with a timelike Wilson line in an arbitrary representation. We show that the theory is equivalent to N fermions with internal degrees of freedom which interact among themselves with a generalized Sutherland-type interaction. By evaluating the expectation value of the Wilson line in the original theory we explicitly find the spectrum and degeneracies of these particle systems.