ON THE CONSISTENCY OF THE EXACT RENORMALIZATION GROUP APPROACH APPLIED TO GAUGE THEORIES IN ALGEBRAIC NONCOVARIANT GAUGES

Abstract

We study a class of Wilsonian formulations of non-Abelian gauge theories in algebraic noncovariant gauges where the Wilsonian infrared cutoff Λ 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 Λ≠0. Then we discuss the infrared limit Λ→0. We show that the singularities of the axial gauge choice are avoided in planar gauge and light-cone gauge. In addition the issue of on-shell divergences is addressed in some explicit example. Finally the rectangular Wilson loop of size 2L×2T is evaluated at lowest order in perturbation theory and a noncommutativity between the limits Λ→0 and T→∞ is pointed out.