Two-dimensional Yang-Mills theory: perturbative and instanton contributions, and its relation to QCD in higher dimensions

TL;DR

This paper explores two-dimensional Yang-Mills theory, comparing perturbative and instanton contributions, and discusses their implications for understanding quantum chromodynamics (QCD) in higher dimensions.

Contribution

It clarifies the roles of light-front and equal-time formulations in 2D Yang-Mills theory and highlights the importance of instantons in the equal-time approach.

Findings

Exact quark-antiquark potential derived in light-front perturbation theory.

Instanton contributions are essential in the equal-time formulation.

Higher-dimensional QCD lacks exact solutions, favoring the equal-time approach.

Abstract

Two different scenarios (light-front and equal-time) are possible for Yang-Mills theories in two dimensions. The exact $\bar q q$-potential can be derived in perturbation theory starting from the light-front vacuum, but requires essential instanton contributions in the equal-time formulation. In higher dimensions no exact result is available and, paradoxically, only the latter formulation (equal-time) is acceptable, at least in a perturbative context.