Remarks on the static potential in theories with Lorentz violation terms

TL;DR

This paper investigates how Lorentz-violating terms alter the static potential in electrodynamics of chiral matter and Abelian Higgs models, revealing logarithmic and new Yukawa potential corrections.

Contribution

It provides the first detailed analysis of static potential modifications due to Lorentz violation in these models using gauge-invariant variables.

Findings

Logarithmic correction to Coulomb potential in chiral electrodynamics

New corrections to Yukawa potential in Lorentz-breaking Abelian Higgs model

Application of gauge-invariant, path-dependent variables formalism

Abstract

We study the impact of Lorentz violating terms on a physical observable for both electrodynamics of chiral matter and an Abelian Higgs-like model in $3+1$ dimensions. Our calculation is done within the framework of the gauge-invariant, but path-dependent, variables formalism. Interestingly enough, for electrodynamics of chiral matter we obtain a logarithmic correction to the usual static Coulomb potential. Whereas for a Abelian Higgs model with a Lorentz-breaking term, our result displays new corrections to the Yukawa potential.