# Dynamical Lorentz symmetry breaking in a tensor bumblebee model

## TL;DR

This paper develops a tensor bumblebee model with a spinor, demonstrating that the one-loop effective potential leads to dynamical Lorentz symmetry breaking, with the potential being positively defined and having a continuous set of minima.

## Contribution

It introduces a new tensor bumblebee model with a spinor coupling that shows dynamical Lorentz symmetry breaking through the one-loop effective potential analysis.

## Key findings

- Effective potential is positively defined.
- Potential has a continuous set of minima.
- Dynamical Lorentz symmetry breaking occurs in the model.

## Abstract

In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor, calculate the one-loop effective potential of the (pseudo)tensor field, and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking. We also argue that, contrarily to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined potential and thus do not allow for the dynamical Lorentz symmetry breaking.