Fermion Masses from the Planck Mass

The "no-go" theorem of Nielsen and Ninomiya, forbidding a sensible formulation of the usual electroweak action on a lattice, has been revised proceeding from the hypothesis that space-time, as a result of the dynamics of quantum gravity, is a four-dimensional random lattice with constant a_p, the Planck length. We find that a sensible electroweak theory at long wave-lengths is recovered by adding a chiral-gauge-invariant quadrilinear fermionic term. Dynamical symmetry breaking of Nambu-Jona-Lasinio (NJL) type is shown to be crucial for making contact with known phenomenology. The relation of this approach to similar recent proposal is briefly discussed.