The spectrum of multi-flavor QCD_2 and the non-Abelian Schwinger equation

TL;DR

This paper investigates the spectrum of massless multi-flavor QCD in two dimensions by solving non-Abelian Schwinger equations, revealing massive mesons and ruling out soliton solutions, thus clarifying baryon absence in the semi-classical limit.

Contribution

It extends the understanding of massless multi-flavor QCD_2 by solving non-Abelian Schwinger equations and proving the non-existence of soliton solutions.

Findings

Massive mesons with specific mass formulae identified

Generalization of non-Abelian solutions achieved

No soliton solutions exist in the semi-classical approximation

Abstract

Massless $QCD_2$ is dominated by classical configurations in the large $N_f$ limit. We use this observation to study the theory by finding solutions to equations of motion, which are the non-Abelian generalization of the Schwinger equation. We find that the spectrum consists of massive mesons with $M^2={e^2 N_f\over 2\pi}$ which correspond to Abelian solutions. We generalize previously discovered non-Abelian solutions and discuss their interpretation. We prove a no-go theorem ruling out the existence of soliton solutions. Thus the semi-classical approximation shows no baryons in the case of massless quarks, a result derived before in the strong-coupling limit only.