On the Consistency of the Exact Renormalization Group Approach Applied to Gauge Theories in Algebraic Non-Covariant Gauges

TL;DR

This paper investigates the consistency of the Wilsonian exact renormalization group approach in non-Abelian gauge theories using algebraic non-covariant gauges, focusing on infrared behavior, gauge dependence, and Wilson loop calculations.

Contribution

It demonstrates how to preserve Ward-Takahashi identities with an infrared cutoff and analyzes the infrared limit and Wilson loop behavior in specific gauges.

Findings

Infrared divergences are manageable in planar and light-cone gauges.

Singularities in axial gauge are avoided in certain non-covariant gauges.

Non-commutativity between limits affects Wilson loop evaluations.

Abstract

We study a class of Wilsonian formulations of non-Abelian gauge theories in algebraic non-covariant gauges where the Wilsonian infrared cutoff $\Lambda$ is inserted as a mass term for the propagating fields. In this way the Ward-Takahashi identities are preserved to all scales. Nevertheless BRST-invariance in broken and the theory is gauge-dependent and unphysical at $\Lambda\neq0$. Then we discuss the infrared limit $\Lambda\to0$. We show that the singularities of the axial gauge choice are avoided in planar gauge and light-cone gauge. In addition the issue of infrared divergences is addressed in some explicit example. Finally the rectangular Wilson loop of size $2L\times 2T$ is evaluated at lowest order in perturbation theory and a non commutativity between the limits $\Lambda\to0$ and $T\to\infty$ is pointed out.