Anomalous Lorentz and CPT violation

TL;DR

This paper explores a mechanism for Lorentz and CPT violation arising from four-dimensional chiral gauge theories on a spacetime with a compact dimension, showing how a Chern-Simons-like term causes symmetry breaking.

Contribution

It demonstrates the emergence of Lorentz and CPT violation through a local Chern-Simons-like term in the effective gauge-field action for Abelian gauge fields on a spacetime with topology $ ext{R}^3 imes S^1$, using both perturbative and nonperturbative methods.

Findings

Lorentz and CPT violation can originate from topological effects in chiral gauge theories.

The violation manifests as a local Chern-Simons-like term in the effective action.

Both perturbative and lattice regularization approaches confirm the anomaly.

Abstract

If there exists Lorentz and CPT violation in nature, then it is crucial to discover and understand the underlying mechanism. In this contribution, we discuss one such mechanism which relies on four-dimensional chiral gauge theories defined over a spacetime manifold with topology $\mathbb{R}^3 \times S^1$ and periodic spin structure for the compact dimension. It can be shown that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. For arbitrary Abelian $U(1)$ gauge fields with trivial holonomies in the compact direction, this anomalous Lorentz and CPT violation has recently been established perturbatively with a Pauli-Villars-type regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.