The spectrum of multi-flavor QCD 2 and the non-abelian Schwinger equation

Abstract

Massless QCD 2 is dominated by classical configurations in the larre- 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 /2 π, 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.