Wilson Loop Area Law for 2D Yang-Mills in Generalized Axial Gauge

TL;DR

This paper proves an area law for Wilson loop expectation values in 2D Yang-Mills theory within a broad class of axial-like gauges, using homotopy invariance of iterated integrals to evaluate second-order perturbative integrals.

Contribution

It establishes an area law for Wilson loops in 2D Yang-Mills across generalized axial gauges, extending previous results and introducing new evaluation techniques.

Findings

Wilson loops obey an area law up to second order

Homotopy invariance simplifies second-order integral evaluation

Results apply to a broad family of axial-like gauges

Abstract

We prove that Wilson loop expectation values for arbitrary simple closed contours obey an area law up to second order in perturbative two-dimensional Yang-Mills theory. Our analysis occurs within a general family of axial-like gauges, which include and interpolate between holomorphic gauge and the Wu-Mandelstam-Liebrandt light cone gauge. Our methods make use of the homotopy invariance properties of iterated integrals of closed one-forms, which allows us to evaluate the nontrivial integrals occurring at second order. We close with a discussion on complex gauge-fixing and deformation of integration cycles for holomorphic path integrals to shed light on some of the quantum field-theoretic underpinnings of our results.