Chiral gauge theories and anomalies in the Wilson renormalization group approach

TL;DR

This paper extends the Wilson renormalization group framework to chiral gauge theories, demonstrating that gauge symmetry can be maintained and the chiral anomaly correctly reproduced without ambiguity in four dimensions.

Contribution

It introduces a method to implement local gauge symmetry in chiral gauge theories within the Wilson RG approach, handling chiral anomalies explicitly.

Findings

Gauge symmetry can be preserved via RG boundary conditions.

The correct chiral anomaly is reproduced in the Wilson RG framework.

No ambiguity arises in handling $ ext{g}_5$ in four dimensions.

Abstract

We extend the Wilson renormalization group (RG) formulation to chiral gauge theories and show that local gauge symmetry can be implemented by a suitable choice of the RG flow boundary conditions. Since the space-time dimension is four, there is no ambiguity in handling the matrix $\g_5$ and left and right fermions are not coupled. As a result the ultraviolet action contains all possible globally chiral invariant interactions. Nevertheless, the correct chiral anomaly is reproduced.