Spontaneous Breaking of Lorentz Symmetry with an antisymmetric tensor

TL;DR

This paper explores how spontaneous Lorentz symmetry breaking via an antisymmetric tensor affects low-energy physics, analyzing stability, causality, and experimental bounds within effective field theories.

Contribution

It introduces a comprehensive effective action for Goldstone modes from Lorentz breaking with an antisymmetric tensor, addressing stability and observational constraints.

Findings

Only one Goldstone mode is dynamical for a consistent low-energy model.

Interaction terms enhance stability and protect against Lorentz violation.

Experimental bounds constrain model parameters.

Abstract

Spontaneous violation of Lorentz symmetry by the vacuum condensation of an antisymmetric $2$-tensor is considered. The coset construction for nonlinear realization of spacetime symmetries is employed to build the most general low-energy effective action for the Goldstone modes interacting with photons. We analyze the model within the context of the Standard-Model Extension and noncommutative QED. Experimental bounds for some parameters of the model are discussed, and we readdress the subtle issues of stability and causality in Lorentz non-invariant scenarios. Besides the two photon polarizations, just one Goldstone mode must be dynamical to set a sensible low-energy effective model, and the enhancement of the stability by accounting interaction terms points to a protection against observational Lorentz violation.