Two-dimensional Yang-Mills theory in the leading 1/N expansion revisited

TL;DR

This paper revisits two-dimensional Yang-Mills theory by solving an integral equation for quark-antiquark bound states, exploring the spectrum's dependence on an interpolation parameter between two known models, revealing qualitative agreement with 't Hooft's results.

Contribution

It provides a formal solution to the bound state integral equation and analyzes the spectrum's behavior across different interpolation parameters, including the special case of Wu's model.

Findings

Spectrum agrees with 't Hooft's model for ta 

Spectrum collapses to zero at ta=1, no Regge trajectories

Explicit approximate spectrum expression for specific coupling-to-mass ratio

Abstract

We obtain a formal solution of an integral equation for $q\bar q$ bound states, depending on a parameter \eta which interpolates between 't Hooft's (\eta=0) and Wu's (\eta=1) equations. We also get an explicit approximate expression for its spectrum for a particular value of the ratio of the coupling constant to the quark mass. The spectrum turns out to be in qualitative agreement with 't Hooft's as long as \eta \neq 1. In the limit \eta=1 (Wu's case) the entire spectrum collapses to zero, in particular no rising Regge trajectories are found.