Exact BRS Symmetry realized on the Renormalization Group Flow

TL;DR

This paper demonstrates that gauge symmetry, reflected by the quantum master equation, is preserved along the Wilsonian renormalization group flow using an average action approach, with explicit one-loop calculations confirming this property.

Contribution

It introduces a continuum analog of the block spin transformation that maintains gauge symmetry and satisfies the quantum master equation along the RG flow.

Findings

Average action satisfies the quantum master equation.

Gauge symmetry is preserved along the RG flow.

Explicit one-loop evaluation confirms the theoretical framework.

Abstract

Using the average action defined with a continuum analog of the block spin transformation, we show the presence of gauge symmetry along the Wilsonian renormalization group flow. As a reflection of the gauge symmetry, the average action satisfies the quantum master equation(QME). We show that the quantum part of the master equation is naturally understood once the measure contribution under the BRS transformation is taken into account. Furthermore an effective BRS transformation acting on macroscopic fields may be defined from the QME. The average action is explicitly evaluated in terms of the saddle point approximation up to one-loop order. It is confirmed that the action satisfies the QME and the flow equation.