Two-dimensional QCD, instanton contributions and the perturbative Wu-Mandelstam-Leibbrandt prescription

TL;DR

This paper explores the relationship between instanton contributions and perturbative results in two-dimensional QCD on a sphere, demonstrating how instantons influence confinement and area law behavior.

Contribution

It shows that considering only the zero-instanton sector reproduces the perturbative series with Wu-Mandelstam-Leibbrandt prescription, clarifying the role of instantons in 2D QCD.

Findings

Instantons are crucial for pure area exponentiation.

Ignoring instantons alters string tension and confinement.

Decompactification limit recovers perturbative series with Wu-Mandelstam-Leibstam prescription.

Abstract

The exact Wilson loop expression for the pure Yang-Mills U(N) theory on a sphere $S^2$ of radius $R$ exhibits, in the decompactification limit $R\to \infty$, the expected pure area exponentiation. This behaviour can be understood as due to the sum over all instanton sectors. If only the zero instanton sector is considered, in the decompactification limit one exactly recovers the sum of the perturbative series in which the light-cone gauge Yang-Mills propagator is prescribed according to Wu-Mandelstam-Leibbrandt. When instantons are disregarded, no pure area exponentiation occurs, the string tension is different and, in the large-N limit, confinement is lost.