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

1/N expansion for Horava–Lifshitz like four-fermion models

“…Some studies in four dimensions with z = 3 have also been realized [18]. Here we extend the three-dimensional studies performed in [16] to the four-dimensional case by considering a class of models with dynamical critical exponents z = 2 and z = 3. From another side, our results generalize studies performed in [18,19] due to consideration of an additional coupling.…”

“…In spite of that, Nambu-Jona-Lasinio like models [14,15] have been used in four dimensions as effective theories to investigate the chiral symmetry breakdown, with cutoffs to control the ultraviolet divergences. Horava-Lifshitz like four fermion models in 2+1 dimensions were analyzed in [16,17]. Some studies in four dimensions with z = 3 have also been realized [18].…”

Bose-Einstein condensation in Hořava-Lifshitz theory

“…Extensions of QED with lifshitz scaling were studied specially in the context of radiative corrections and renormalization [21,22]. HL-like extensions for Gross-Neveu [23] and four-fermions [24][25][26] models were also studied. The finite temperature effects were studied in HL-like extensions of the scalar QED and for Yukawa coupling [27].…”