1+1 Dimensional Yang-Mills Theories in Light-Cone Gauge

TL;DR

This paper compares two formulations of 1+1 dimensional SU(N) Yang-Mills theories in light-cone gauge, highlighting differences in results and discontinuities in higher dimensions, supported by Wilson loop and bound state analyses.

Contribution

It demonstrates that only one formulation aligns with Feynman gauge results and reveals discontinuities in the theory as dimensions approach two.

Findings

One formulation matches Feynman gauge results.

Discontinuity observed in the D→2 limit.

Wilson loop calculations support the findings.

Abstract

In 1+1 dimensions two different formulations exist of SU(N) Yang Mills theories in light-cone gauge; only one of them gives results which comply with the ones obtained in Feynman gauge. Moreover the theory, when considered in 1+(D-1) dimensions, looks discontinuous in the limit D=2. All those features are proven in Wilson loop calculations as well as in the study of the $q\bar q$ bound state integral equation in the large N limit.