No one-loop gauge anomalies for a Lorentz-violating quantum electrodynamics: Evaluation of the three-photon vertex

TL;DR

This paper verifies that the three-photon vertex in a Lorentz-violating extension of quantum electrodynamics does not produce gauge anomalies, completing the analysis of potential anomaly sources in the theory.

Contribution

The study explicitly evaluates the three-photon vertex for anomalies, confirming its anomaly-free nature in Lorentz-violating quantum electrodynamics.

Findings

Three-photon vertex is free of gauge anomalies.

All potential anomaly diagrams are verified to be anomaly-free.

Completes the anomaly analysis for the theory.

Abstract

Identification of the diagrams that can lead to gauge anomalies in the (minimal) Lorentz- and $CPT$-violating extension of quantum electrodynamics reveals these are the electron self-energy and vertex correction (related to the Ward-Takahashi identity), the photon self-energy (related to the vacuum polarization tensor transversality), and the three-photon vertex diagrams. All but the latter were explicitly verified to be free of anomalies to first order in loop expansion. Here we provide this remaining evaluation and verify the absence of anomalies in this process.