Nonperturbative renormalization of the lattice Sommerfield vector model

TL;DR

This paper proves nonperturbatively that the lattice Sommerfield model exhibits no infinite field renormalization and non-renormalized anomalies, supporting its consistency with Standard Model properties.

Contribution

It provides a nonperturbative proof of the absence of infinite field renormalization and anomaly renormalization in the lattice Sommerfield model, aligning with Standard Model features.

Findings

No infinite field renormalization in the model

Anomalies are non-renormalized

Gauge invariant observables have convergent expansions

Abstract

The lattice Sommerfield model, describing a massive vector gauge field coupled to a light fermion in 2d, is an ideal candidate to verify perturbative conclusions. In contrast with continuum exact solutions, we prove that there is no infinite field renormalization, implying the reduction of the degree of the ultraviolet divergence, and that anomalies are non renormalized. Such features are the counterpart of analogue properties at the basis of the Standard model perturbative renormalizability. The results are non-perturbative, in the sense that the averages of gauge invariant observables are expressed in terms of convergent expansions uniformly in the lattice and volume.