Universality of the Axial Anomaly in Lattice QCD

TL;DR

This paper proves that lattice QCD naturally reproduces the axial anomaly in the continuum limit under broad conditions, confirming the universality of this phenomenon across different lattice formulations.

Contribution

It establishes a general proof that the axial anomaly arises in lattice QCD, including Ginsparg-Wilson fermions, under minimal assumptions, extending to SU(N) gauge theories.

Findings

Lattice QCD reproduces the axial anomaly in the continuum limit.

The proof applies to Ginsparg-Wilson fermions and general lattice actions.

The results confirm the universality of the axial anomaly in lattice gauge theories.

Abstract

We prove that lattice QCD generates the axial anomaly in the continuum limit under very general conditions on the lattice action, which includes the case of Ginsparg-Wilson fermions. The ingredients going into the proof are gauge invariance, locality of the Dirac operator, absence of fermion doubling, the general form of the lattice Ward identity, and the power counting theorem of Reisz. The results generalize in an obvious way to SU(N) lattice gauge theories.