Asymptotically free four-fermi theory in 4 dimensions at the z=3 Lifshitz-like fixed point

TL;DR

This paper demonstrates that a four-fermion theory at a Lifshitz-like fixed point in 3+1 dimensions is asymptotically free, generates mass dynamically, and could provide a novel approach to the fermion mass problem and electroweak symmetry breaking.

Contribution

It introduces a nonperturbative, ultra-violet complete four-fermion model at z=3 fixed point with emergent Lorentz invariance and potential applications to particle physics.

Findings

The theory is asymptotically free at the Lifshitz fixed point.

Mass scale is generated dynamically without a Higgs potential.

The axial anomaly matches the relativistic case at z=3.

Abstract

We show that a Nambu-Jona-Lasinio type four-fermion coupling at the z=3 Lifshitz-like fixed point in 3+1 dimensions is asymptotically free and generates a mass scale dynamically. This result is nonperturbative in the limit of a large number of fermion species. The theory is ultra-violet complete and at low energies exhibits Lorentz invariance as an emergent spacetime symmetry. Many of our results generalize to z=d in odd d spatial dimensions; z=d=1 corresponds to the Gross-Neveu model. The above mechanism of mass generation has potential applications to the fermion mass problem and to dynamical electroweak symmetry breaking. We present a scenario in which a composite Higgs field arises from a condensate of these fermions, which then couples to quarks and leptons of the standard model. Such a scenario could eliminate the need for the Higgs potential and the associated hierarchy problem. We also show that the axial anomaly formula at z=3 coincides with the usual one in the relativistic domain.