Anomaly cancellation condition in an effective nonperturbative electroweak theory

Abstract

We consider an effective lattice electroweak model composed by a family of elementary particles (two quarks and two leptons) with a quartic interaction describing the weak forces and an interaction with the e.m. field: the lattice step plays the role of the ultraviolet cut-off, the fermions are massless and the photon is massive. The correlations are analytic uniformly in the infinite volume limit provided that the cut-off is of the order of the gauge masses. The electric charges are not renormalized by the interaction and the hypercharge current conservation requirement, up to subdominant corrections, implies the anomaly cancellation condition, partially explaining charge universality.

Vanishing of the anomaly in lattice chiral gauge theory

“…The anomaly cancellation condition is the same as in the continuum case. The lattice regularization plays an essential role; with momentum one a much weaker result holds [15]. (4) Anomalies are strongly connected with transport properties in condensed matter [16]- [18] and we use indeed techniques recently developed for the proof of universality properties in metals to the anomaly cancellation on a lattice [19]- [27].…”