CPT, Lorentz invariance and anomalous clash of symmetries

TL;DR

This paper investigates the role of Lorentz symmetry in quantum anomalies, demonstrating that Lorentz violation does not influence the symmetry clash responsible for anomalies in fermionic theories.

Contribution

It shows that Lorentz symmetry does not contribute to the anomaly clash, even when Lorentz-violating operators are included, clarifying the symmetry's role in anomaly formation.

Findings

Lorentz symmetry does not participate in anomaly clashes.

Lorentz-violating operators do not affect anomaly emergence.

A semiclassical argument illustrates the origin of this independence.

Abstract

In this paper we first discuss the analysis regarding the role of Lorentz symmetry in the perturbative non-gravitational anomalies for a family of fermions, which has been recently performed in arXiv:0809.0184. The theory is assumed to be translational invariant, power-counting renormalizable and based on a local action, but is allowed to have general Lorentz violating operators, including those that break CPT. The main result is that Lorentz symmetry does not participate in the clash of symmetries that leads to the anomalies. Moreover, here we provide a simple "semiclassical" argument that shortly illustrates the origin of this fact.