# Effective potential in Lorentz-breaking field theory models

## TL;DR

This paper explicitly calculates the one-loop effective potential in Lorentz-breaking field theories, including Yukawa-like models and Lorentz-violating scalar QED extensions, showing how Lorentz violation influences quantum corrections.

## Contribution

It provides the first explicit calculations of the effective potential in Lorentz-violating models, demonstrating the dependence on background tensors and the restoration limit of Lorentz symmetry.

## Key findings

- Effective potential converges to known results when Lorentz symmetry is restored.
- One-loop corrections depend on Lorentz-violating background tensors.
- Implications for physical quantities like induced mass via Coleman-Weinberg mechanism.

## Abstract

We calculate explicitly the one-loop effective potential in different Lorentz-breaking field theory models. First, we consider a Yukawa-like theory and, then, some examples of Lorentz-violating extensions of scalar QED. We observed, for the extended QED models, that the resulting effective potential converges to the known result in the limit in which Lorentz-symmetry is restored. Besides, the one-loop corrections to the effective potential in all the cases we studied depend on the background tensors responsible for the Lorentz symmetry violation. This have consequences in physical quantities like, for example, in the induced mass due to Coleman-Weinberg mechanism.