Dynamical Lorentz and CPT symmetry breaking in a 4D four-fermion model

TL;DR

This paper investigates how radiative corrections in a 4D four-fermion model can lead to spontaneous Lorentz and CPT symmetry breaking, resulting in a dynamical generation of a Chern-Simons term.

Contribution

It demonstrates that a chiral Thirring model can spontaneously break Lorentz and CPT symmetries through radiative effects, introducing a novel dynamical mechanism.

Findings

Nonzero vacuum expectation value of chiral current triggers symmetry breaking.

Spontaneous Lorentz and CPT violation are demonstrated.

A bumblebee-like model with a Chern-Simons term is dynamically induced.

Abstract

In a 4D chiral Thirring model we analyse the possibility that radiative corrections may produce spontaneous breaking of Lorentz and CPT symmetry. By studying the effective potential, we verified that the chiral current $\bar\psi\gamma^{\mu} \gamma_5 \psi$ may assume a nonzero vacuum expectation value which triggers the Lorentz and CPT violations. Furthermore, by making fluctuations on the minimum of the potential we dynamically induce a bumblebee like model containing a Chern-Simons term.