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

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. Many of our results generalize to z = d in odd d spatial dimensions; z = d = 1 corresponds to the Gross-Neveu model. The mechanism of mass generation discussed here has possible applications to the fermion mass problem and to dynamical electroweak symmetry breaking, in a manner similar to technicolour theories, but without requiring the technicolour gauge bosons.