Generalized CP from non-invertible selection rules

TL;DR

This work develops a CP-invariant framework where fields are labeled by conjugacy-class basis elements of a fusion algebra with non-invertible selection rules. A Z2 symmetry identified with charge conjugation, combined with parity, defines generalized CP, further enriched by flavor symmetries to yield G_f ⋊ Z2^CP. The authors demonstrate that CP-invariant couplings become real and show how spontaneous CP violation can generate CKM/PMNS phases while preserving texture-zero Yukawa structures. Concrete examples based on Z3 gauging of Z7 and related flavor symmetries illustrate how three-zero textures arise and persist, offering a CP-consistent route to flavor phenomenology and a discussion of strong CP implications.

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.