# Anomaly non-renormalization in interacting Weyl semimetals

## TL;DR

This paper proves that the quadratic response of Weyl semimetals' quasi-particle flow is universal and unaffected by interactions, extending the non-renormalization property of the chiral anomaly to lattice models.

## Contribution

It establishes a non-perturbative proof of anomaly non-renormalization in interacting Weyl semimetals on a lattice, near critical points.

## Key findings

- Quadratic response is interaction-independent
- Universality extends to lattice and non-perturbative regimes
- Proof applies near Weyl point merging transition

## Abstract

Weyl semimetals are 3D condensed matter systems characterized by a degenerate Fermi surface, consisting of a pair of `Weyl nodes'. Correspondingly, in the infrared limit, these systems behave effectively as Weyl fermions in $3+1$ dimensions. We consider a class of interacting 3D lattice models for Weyl semimetals and prove that the quadratic response of the quasi-particle flow between the Weyl nodes is universal, that is, independent of the interaction strength and form. Universality is the counterpart of the Adler-Bardeen non-renormalization property of the chiral anomaly for the infrared emergent description, which is proved here in the presence of a lattice and at a non-perturbative level. Our proof relies on constructive bounds for the Euclidean ground state correlations combined with lattice Ward Identities, and it is valid arbitrarily close to the critical point where the Weyl points merge and the relativistic description breaks down.