# Emergent gauge bosons and dynamical symmetry breaking in a four-fermion Lifshitz model

## TL;DR

This paper studies a four-fermion Lifshitz model, showing how an auxiliary vector field's effective dynamics can lead to spontaneous rotational symmetry breaking through a one-loop generated potential.

## Contribution

It introduces an auxiliary vector field in the Lifshitz four-fermion model and demonstrates the emergence of a bumblebee potential causing dynamical symmetry breaking.

## Key findings

- Effective bumblebee potential arises as a one-loop correction.
- Dynamical breaking of rotational symmetry is demonstrated.
- Effective dynamics for the auxiliary vector field is explicitly derived.

## Abstract

We consider the four-fermion Lifshitz model, introduce in this model an auxiliary vector field, and generate an effective dynamics for this field. We explicitly demonstrate that within this dynamics, the effective bumblebee potential for the vector field naturally arises as a one-loop correction and allows for the dynamical breaking of the rotational symmetry.