Regularized path integrals and anomalies -- U(1) chiral gauge theory

TL;DR

This paper investigates how regularized path integrals reveal the origin of the Adler anomaly in chiral U(1) gauge theory, showing that gauge symmetry violations manifest in the three-photon amplitude and cannot be restored in the UV limit.

Contribution

It demonstrates how anomalies appear in regularized path integrals for chiral U(1) gauge theory and links infrared nonanalyticity to gauge symmetry violation.

Findings

Three-photon amplitude violates Slavnov-Taylor identities

Anomaly manifests as non-restorable gauge symmetry violation

Infrared nonanalyticity is related to anomaly emergence

Abstract

We analyse the origin of the Adler anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [1]. Here we analyse U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor-Identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.