Comment on the claim of physical irrelevance of the topological term

TL;DR

The paper addresses whether CP-violating effects from the topological $\Theta$-term in QCD can be absent; it analyzes the path-integral formulation with $\frac{\theta}{16\pi^2} \int \mathrm{Tr} G \wedge G$ and its associated topological charge $Q$, including the role of instantons and large gauge transformations. It argues that CP violation persists in physical observables, and that finite-volume and boundary-condition analyses do not remove the $\theta$-dependence; fixed-$Q$ approaches recover the $\theta$-dependent physics in the large-volume limit, consistent with lattice results. The conclusion reinforces the standard understanding of topological effects in non-Abelian gauge theories, supports the continued interpretation of experimental constraints on $\theta$ (e.g., the neutron EDM), and preserves the relevance of axion physics as a dynamical counterterm.

Abstract

We argue that the claim of the absence of charge-conjugation-parity (CP) violating effects due to a topological term in quantum chromodynamics (QCD) is based upon a misunderstanding, and the standard results in the field are correct.