Emergent Adler-Bardeen theorem

TL;DR

This paper proves that the Adler-Bardeen non-renormalization theorem holds non-perturbatively in certain lattice QED models with emergent symmetries, ensuring the anomaly remains unaffected by radiative corrections.

Contribution

It introduces a new non-perturbative technique combining renormalization group methods and Ward identities to establish the AB theorem on the lattice.

Findings

Radiative corrections to the anomaly vanish at finite lattice

The AB property is robust against symmetry breaking corrections

The technique applies to models with emergent Lorentz or chiral symmetry

Abstract

We consider a QED$_{d+1}$, $d=1,3$ lattice model with emergent Lorentz or chiral symmetry, both when the interaction is irrelevant or marginal. While the correlations present symmetry breaking corrections, we prove that the Adler-Bardeen (AB) non-renormalization property holds at a non-perturbative level even at finite lattice: all radiative corrections to the anomaly are vanishing. The analysis uses a new technique based on the combination of non-perturbative regularity properties obtained by exact renormalization Group methods and Ward Identities. The AB property, essential for the renormalizability of the standard model, is therefore a robust feature imposing no constraints on possible symmetry breaking terms, at least in the class of lattice models considered.