Spontaneous Breakdown of the Lorentz Invariance

TL;DR

This paper investigates how Lorentz invariance can be spontaneously broken in a 3D gauge theory with a Chern-Simons term, highlighting the role of magnetic fields and spectral flow in this process.

Contribution

It demonstrates the dynamical generation of magnetic fields leading to Lorentz symmetry breaking and explores the associated spectral flow and instabilities in Chern-Simons theories.

Findings

Magnetic fields can spontaneously break Lorentz invariance in 3D gauge theories.

Spectral flow is crucial in understanding the symmetry breaking mechanism.

Pure Chern-Simons theory exhibits instability related to this phenomenon.

Abstract

We re-examine three-dimensional gauge theory with a Chern-Simons term in which the Lorentz invariance is spontaneously broken by dynamical generation of a magnetic field. A non-vanishing magnetic field leads, through the Nambu-Goldstone theorem, to the decrease of zero-point energies of photons, which accounts for a major part of the mechanism. The asymmetric spectral flow plays an important role. The instability in pure Chern-Simons theory is also noted.