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The anomaly cancellation is a basic property of the Standard Model, crucialfor its consistence. We consider a lattice chiral gauge theory of masslessWilson fermions interacting with a non-compact massive U(1) field coupled withleft and right handed fermions in four dimensions. We prove in the infinitevolume limit, for weak coupling and inverse lattice step of the order of bosonmass, that the anomaly vanishes up to subleading corrections and under the samecondition as in the continuum. The proof is based on a combination of exactRenormalization Group, non perturbative decay bounds of correlations andlattice symmetries.

Vanishing of the anomaly in lattice chiral gauge theory