Weighted power counting and Lorentz violating gauge theories. II: Classification

TL;DR

This paper classifies Lorentz-violating gauge theories that are renormalizable via weighted power counting, demonstrating their structural properties and conditions for renormalization of complex interactions.

Contribution

It provides a comprehensive classification of Lorentz-violating gauge theories with detailed analysis of their renormalization properties and structural constraints.

Findings

Renormalization does not generate higher time derivatives.

Conditions for renormalizing non-renormalizable vertices are established.

Several four-dimensional examples are provided.

Abstract

We classify the local, polynomial, unitary gauge theories that violate Lorentz symmetry explicitly at high energies and are renormalizable by weighted power counting. We study the structure of such theories and prove that renormalization does not generate higher time derivatives. We work out the conditions to renormalize vertices that are usually non-renormalizable, such as the two scalar-two fermion interactions and the four fermion interactions. A number of four dimensional examples are presented.