Understanding Chiral Anomaly in Coordinate Space

TL;DR

This paper revisits the chiral anomaly, expressing it as a coordinate space integral of chiral currents and identifying a key local counterterm through an integrability condition.

Contribution

It provides a novel coordinate space formulation of the chiral anomaly, extending Wilson's earlier discussions and highlighting the role of a finite local counterterm.

Findings

Chiral anomaly expressed as a double integral in coordinate space.

Identification of a finite local counterterm via integrability condition.

Clarification of the anomaly's structure in terms of three-point functions.

Abstract

By completing the old discussion of K.~Wilson, we express the chiral anomaly in terms of a double integral of a three-point function of chiral currents over an arbitrarily small region in the coordinate space. An integrability condition provides an important finite local counterterm to the integral.