Regularized Quantum Master Equation in the Wilsonian Renormalization Group

TL;DR

This paper analyzes the quantum master equation within the Wilsonian renormalization group framework, showing how gauge symmetry is preserved or broken by anomalies, using Pauli-Villars regularization and Jacobian calculations.

Contribution

It introduces a perturbative approach to the QME for the Wilsonian effective action, linking gauge symmetry realization to the Jacobian factor and anomalies along the RG flow.

Findings

QME determines gauge symmetry preservation during RG flow.

Non-vanishing  indicates BRS anomaly preservation.

Jacobian calculation for Yang-Mills theory confirms anomaly-free conditions.

Abstract

Using the Pauli-Villars regularization, we make a perturbative analysis of the quantum master equation (QME), $\Sigma =0$, for the Wilsonian effective action. It is found that the QME for the UV action determines whether exact gauge symmetry is realized along the renormalization group (RG) flow. The basic task of solving the QME can be reduced to compute the Troost-van Niuwenhuizen-Van Proyen jacobian factor for the classical UV action. When the QME cannot be satisfied, the non-vanishing $\Sigma$ is proportional to a BRS anomaly, which is shown to be preserved along the RG flow. To see how the UV action fulfills the QME in anomaly free theory, we calculate the jacobian factor for a pure Yang-Mills theory in four dimensions.