Non-renormalization of the 'chiral anomaly' in interacting lattice Weyl semimetals

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, which is the
condensed matter analogue of the chiral anomaly in QED4, is universal,
that is, independent of the interaction strength and form. Universality,
which is the counterpart of the Adler-Bardeen non-renormalization
property of the chiral anomaly for the infrared emergent description, is
proved to hold at a non-perturbative level, notwithstanding the presence
of a lattice (in contrast with the original Adler-Bardeen theorem, which
is perturbative and requires relativistic invariance to hold). The proof
relies on constructive bounds for the Euclidean ground state correlation
functions 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.
Joint work with V. Mastropietro and M. Porta.