On the Horava-Lifshitz-like Gross-Neveu model

TL;DR

This paper reformulates the Gross-Neveu model with Horava-Lifshitz scaling in (2+1) dimensions, analyzing its gap equation, parity breaking, and renormalizability, revealing distinct behaviors for even and odd critical exponents z.

Contribution

It introduces a Horava-Lifshitz-like version of the Gross-Neveu model, studies its gap equation at finite temperature, and demonstrates renormalizability and parity breaking phenomena depending on z.

Findings

Parity breaking occurs only for odd z.

A critical temperature exists where parity breaking ceases.

The model remains renormalizable within 1/N expansion.

Abstract

We describe a Horava-Lifshitz-like reformulated four-fermion Gross-Neveu model describing the dynamics of two-component spinors in (2+1)-dimensional space-time. Within our study, we introduce the Lagrange multiplier, study the gap equation (including the finite temperature case) which turns out to display essentially distinct behaviors for even and odd values of the critical exponent z, and show that the dynamical parity breaking occurs only for the odd z. We demonstrate that for any odd z, there exists a critical temperature at which the dynamical parity breaking disappears. Besides of this, we obtain the effective propagator and show that the resulting effective theory is renormalizable within the framework of the 1/N expansion for all values of z. As one more application of the dynamical parity breaking, we consider coupling of the vector field to the fermions in the case of a simplified spinor-vector coupling and discuss the generation the Chern-Simons term.