Anomalies in the ERG Approach

TL;DR

This paper explores how the antifield formalism within the exact renormalization group framework can describe symmetries and anomalies, linking the quantum master operator to the Wess-Zumino condition.

Contribution

It demonstrates the utility of the antifield formalism in the ERG approach for analyzing gauge symmetries and anomalies, establishing algebraic relations with the Wess-Zumino condition.

Findings

Quantum master operator vanishes when symmetry is present

Algebraic relation of QM operator relates to Wess-Zumino condition

Anomalies influence the quantum master operator

Abstract

The antifield formalism adapted in the exact renormalization group is found to be useful for describing a system with some symmetry, especially the gauge symmetry. In the formalism, the vanishing of the quantum master operator implies the presence of a symmetry. The QM operator satisfies a simple algebraic relation that will be shown to be related to the Wess-Zumino condition for anomalies. We also explain how an anomaly contributes to the QM operator.