On the Horava-Lifshitz-like Gross-Neveu model

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.

arXiv comment15 pages, version accepted to Physical Review D, misprint corrected

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• Horava-Lifshitz four-fermion model revisited and dynamical symmetry breaking
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• 1/N Expansion for Horava-Lifshitz like four-fermion models
• One-loop corrections in the z=3 Lifshitz extension of QED
• Bose-Einstein condensation in Hořava-Lifshitz theory
• Emergent gauge bosons and dynamical symmetry breaking in a four-fermion Lifshitz model
• CPT-violating z=3 Horava-Lifshitz QED and generation of the Carroll-Field-Jackiw term
• Generation of Carroll-Field-Jackiw term in the Functional Integral approach within Horava-Lifshitz $z=3$ CPT-violating QED