Unobservability of topological charge in nonabelian gauge theory

Abstract

We show that the topological charge of nonabelian gauge theory is unphysical by using the fact that it always involves the unphysical gauge field component proportional to the gradient of the gauge function. The removal of Gribov copies, which may break the Becchi-Rouet-Stora-Tyutin symmetry, is irrelevant thanks to the perturbative one-loop finiteness of the chiral anomaly. The unobservability of the topological charge immediately leads to the resolution of the Strong CP problem. We also present important consequences such as the physical relevance of axial $U(1)$ symmetry, the $\theta$-independence of vacuum energy, the unphysicalness of topological instantons, and the impossibilities of realizing the sphaleron induced baryogenesis as well as the chiral magnetic effect. The unphysical vacuum angle and the axial $U(1)$ symmetry also imply that the CP phase of the Cabibbo-Kobayashi-Maskawa matrix is the sole source of CP violation of the standard model.

Comments: 5 pages, no figures. Letter. It will be followed by a full paper. Slides explaining graphically the discussion are given in https://www2.yukawa.kyoto-u.ac.jp/~nodoka.yamanaka/topologicalcharge/index.html