The Wilson Loop in Yang-Mills Theory in the General Axial Gauge

TL;DR

This paper computes a Wilson loop in Yang-Mills theory within a unified axial gauge formalism, demonstrating gauge independence and consistency with Feynman gauge results at one-loop order.

Contribution

It introduces a novel calculation method using distinct vector sets for the path and gauge-fixing, validating the unified-gauge formalism at one-loop order.

Findings

Wilson loop result is independent of the gauge vector $N_$

Results agree numerically with Feynman gauge calculations

The formalism encompasses various axial gauges within a unified framework

Abstract

We test the unified-gauge formalism by computing a Wilson loop in Yang-Mills theory to one-loop order. The unified-gauge formalism is characterized by the abritrary, but fixed, four-vector $N_\mu$, which collectively represents the light-cone gauge $(N^2 = 0)$, the temporal gauge $(N^2 > 0)$, the pure axial gauge $(N^2 < 0)$ and the planar gauge $(N^2 < 0)$. A novel feature of the calculation is the use of distinct sets of vectors, $\{ n_{\mu}, n_{\mu}^{\ast} \}$ and $\{N_{\mu}, N_{\mu}^{\ast}\}$, for the path and for the gauge-fixing constraint, respectively. The answer for the Wilson loop is independent of $N_{\mu}$, and agrees numerically with the result obtained in the Feymman gauge.