The absence of global anomalies of CP symmetry

TL;DR

This paper investigates whether CP symmetry can be gauged without introducing anomalies, finding that for connected, simply connected gauge groups, no new anomalies arise, supporting the consistency of certain CP symmetry solutions.

Contribution

It demonstrates that gauging CP symmetry in theories with connected, simply connected gauge groups does not lead to additional anomalies, including in the Standard Model.

Findings

Gauging CP symmetry does not produce new anomalies for connected, simply connected gauge groups.

Standard Model matter content is free of CP anomalies.

Supports the viability of CP symmetry as a gauge symmetry in certain models.

Abstract

Some solutions to the strong CP problem assume that CP symmetry is a gauge symmetry, which is then spontaneously broken. For this scenario to be possible, the CP symmetry should not have any nonperturbative (global) anomalies. In this paper, we study anomalies of CP symmetry of fermions which are coupled to gravity and gauge fields with a gauge group $G$. When $G$ is connected and simply connected, we show that gauging a CP symmetry does not produce any new anomaly beyond the one before gauging it. In particular, the standard model matter content does not have anomalies.