Generalized CP from non-invertible selection rules

TL;DR

This paper develops a framework for generalized CP symmetry in systems with non-invertible fusion rules, especially those labeled by conjugacy classes of finite groups, and explores implications for CP violation and Yukawa textures.

Contribution

It introduces a novel approach to defining CP symmetry in non-invertible fusion rule systems, linking group-based flavor symmetries with generalized CP transformations.

Findings

CP-invariant systems can be consistently defined with non-invertible fusion rules.

Combining flavor symmetries with CP leads to a generalized CP transformation.

Spontaneous CP violation is possible within this framework.

Abstract

We study a framework in which fields are labeled by basis elements of a fusion algebra with non-invertible fusion rules. In particular, we consider the case where fields are labeled by conjugacy classes of a finite group rather than its irreducible representations. When the fusion rules possess a $\mathbb{Z}_2$ symmetry identified with charge conjugation, a CP-invariant system can be consistently defined together with parity transformation. Furthermore, it is found that combining group-based flavor symmetries underlying non-invertible selection rules with CP symmetry naturally leads to a generalized CP transformation. We also demonstrate the possibility of spontaneous CP violation in this framework and discuss its implications for Yukawa textures.