Effective electromagnetic actions for Lorentz violating theories exhibiting the axial anomaly

TL;DR

This paper calculates the CPT odd electromagnetic effective action in Lorentz-violating fermionic systems with axial anomaly, highlighting the role of LIV parameters and applying the results to tilted Weyl semimetals.

Contribution

It introduces a method to compute LIV contributions to the electromagnetic action considering chemical potential effects, extending understanding of axion electrodynamics in such systems.

Findings

LIV parameters influence the axion coupling in effective actions.

The CPT odd contribution depends on chemical potential and temperature.

Preliminary application to tilted Weyl semimetals demonstrates practical relevance.

Abstract

The CPT odd contribution to the effective electromagnetic action deriving from the vacuum polarization tensor in a large class of fermionic systems exhibiting Lorentz invariance violation (LIV) is calculated using thermal field theory methods, focusing upon corrections depending on the chemical potential. The systems considered exhibit the axial anomaly and their effective actions are described by axion electrodynamics whereby all the LIV parameters enter in the coupling $\Theta(x)$ to the unmodified Pontryagin density. A preliminary application to type-I tilted Weyl semimetals is briefly presented.