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Nonperturbative renormalization of the lattice Sommerfield vector model

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.