# Anomalous Lorentz and CPT violation from a local Chern-Simons-like term in the effective gauge-field action

## TL;DR

This paper demonstrates that in certain four-dimensional chiral gauge theories with a compact dimension, the effective gauge-field action includes a local Chern-Simons-like term that breaks Lorentz and CPT symmetry, confirmed through perturbative and nonperturbative methods.

## Contribution

It provides the first calculation showing Lorentz and CPT violation via a local Chern-Simons-like term in the effective gauge action of chiral gauge theories on $ ext{R}^3 imes S^1$.

## Key findings

- Effective gauge action contains a Lorentz and CPT violating Chern-Simons-like term.
- The result is confirmed both perturbatively and nonperturbatively.
- The violation arises in theories with a compact spatial dimension and trivial holonomies.

## Abstract

We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology $\mathbb{R}^3 \times S^1$ and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian $U(1)$ gauge fields $A_{\mu}(x)$ which depend on all four spacetime coordinates (including the coordinate $x^{4}\in S^1$ of the compact dimension) and have vanishing components $A_{4}(x)$ (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli-Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.