Horava-Lifshitz four-fermion model revisited and dynamical symmetry breaking

TL;DR

This paper investigates dynamical symmetry breaking in a Horava-Lifshitz four-fermion model at z=3, showing Lorentz symmetry emergence and potential positivity across dimensions, with Chern-Simons term generation in three dimensions.

Contribution

It provides a detailed analysis of symmetry breaking and Lorentz symmetry emergence in the Horava-Lifshitz four-fermion model, including the generation of a Chern-Simons term in three dimensions.

Findings

Lorentz symmetry can be dynamically generated in the model.

The model exhibits a positively defined potential.

In three dimensions, a Lorentz invariant Chern-Simons term is generated.

Abstract

In this paper, we develop studies of the dynamical symmetry breaking in the Horava-Lifshitz four-fermion model for the specific case $z=3$ and explicitly demonstrate that for various space-time dimensions, one could arrive at the theory displaying both dynamical generation of the Lorentz symmetry for the kinetic term and arising the positively defined potential at the same time. At the same time, for $D=3$, the Lorentz invariant Chern-Simons term is generated.