Relaxing Lorentz invariance in general perturbative anomalies

TL;DR

This paper investigates how Lorentz symmetry influences perturbative anomalies in fermionic theories, demonstrating that Lorentz violation does not alter the fundamental anomaly cancellation conditions.

Contribution

It shows that Lorentz symmetry is not essential for the structure of perturbative anomalies, and anomaly cancellation conditions remain valid even with Lorentz-violating operators.

Findings

Lorentz violation does not affect anomaly structure.

Anomaly cancellation conditions are regulator-independent.

Lorentz invariance is not required for anomaly consistency.

Abstract

We analyze the role of Lorentz symmetry in the perturbative non-gravitational anomalies for a single family of fermions. 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. We study the conservation of global and gauge currents associate with general internal symmetry groups and find, by using a perturbative approach, that Lorentz symmetry does not participate in the clash of symmetries that leads to the anomalies. We first analyze the triangle graphs and prove that there are regulators for which the anomalous part of the Ward identities exactly reproduces the Lorentz invariant case. Then we show, by means of a regulator independent argument, that the anomaly cancellation conditions derived in Lorentz invariant theories remain necessary ingredients for anomaly freedom.