Constrained Gauge Fields from Spontaneous Lorentz Violation

TL;DR

This paper demonstrates that spontaneous Lorentz violation via a nonlinear vector constraint naturally produces gauge-invariant theories like QED and Yang-Mills, with Lorentz violation appearing only in couplings but not in physical observables.

Contribution

It shows that a nonlinear vector constraint inducing Lorentz violation leads to gauge theories with no physical Lorentz violation, unifying Goldstone bosons with gauge fields in a novel way.

Findings

Massless vector Goldstone bosons emerge from Lorentz violation.

The resulting theories are essentially gauge-invariant and resemble QED and Yang-Mills.

Physical Lorentz invariance is preserved despite Lorentz-violating couplings.

Abstract

Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type $A_{\mu}A^{\mu}=M^{2}$ ($M$ is the proposed scale for Lorentz violation) is shown to generate massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory proves to be QED with a massless vector Goldstone boson naturally associated with the photon, while the non-Abelian symmetry case results in a conventional Yang-Mills theory. These theories, both Abelian and non-Abelian, look essentially nonlinear and contain particular Lorentz (and $CPT$) violating couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical Lorentz violation due to the simultaneously generated gauge invariance.