Weighted power counting and Lorentz violating gauge theories. I: General properties

TL;DR

This paper develops Lorentz-violating gauge theories with improved high-energy behavior through weighted power counting, focusing on their properties, regularity, and potential low-energy Lorentz invariance recovery.

Contribution

It introduces a class of local, unitary gauge theories with explicit Lorentz violation at high energies, employing higher space derivatives without higher time derivatives, and analyzes their properties.

Findings

Gauge theories with weighted power counting are renormalizable and unitary.

The regularity of propagators favors a specific spacetime symmetry breaking.

Discussion on how Lorentz invariance might be recovered at low energies.

Abstract

We construct local, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. They contain higher space derivatives, which improve the behavior of propagators at large momenta, but no higher time derivatives. We show that the regularity of the gauge-field propagator privileges a particular spacetime breaking, the one into into space and time. We then concentrate on the simplest class of models, study four dimensional examples and discuss a number of issues that arise in our approach, such as the low-energy recovery of Lorentz invariance.