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

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.