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

Understand

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.