Exact Renormalization Group in Algebraic Noncovariant Gauges

TL;DR

This paper explores a Wilsonian approach to non-Abelian gauge theories in algebraic noncovariant gauges, analyzing the infrared limit, gauge dependence, and Wilson loop behavior at lowest order.

Contribution

It introduces a Wilsonian formulation with an infrared cutoff in algebraic noncovariant gauges, preserving Ward-Takahashi identities and analyzing gauge singularities and Wilson loop limits.

Findings

Singularities avoided in planar and light-cone gauges

Gauge dependence persists at finite cutoff

Noncommutativity between limits $\Lambda o0$ and $T o ext{infinity}$

Abstract

I study a class of Wilsonian formulations of non-Abelian gauge theories in algebraic noncovariant 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 the BRS-invariance in broken and the theory is gauge-dependent and unphysical at $\Lambda\neq0$. Then I discuss the infrared limit $\Lambda\to0$. I show that the singularities of the axial gauge choice are avoided in planar gauge and in light-cone gauge. Finally the rectangular Wilson loop of size $2L\times 2T$ is evaluated at lowest order in perturbation theory and a noncommutativity between the limits $\Lambda\to0$ and $T\to\infty$ is pointed out.