On discrete gauging and non-invertible selection rules

TL;DR

This paper explores the complex selection rules arising from conjugacy classes in finite discrete groups, revealing new coupling rules influenced by automorphisms and non-group-like behaviors.

Contribution

It clarifies the nature of selection rules in discrete groups, highlighting the role of automorphisms and introducing novel coupling selection rules based on conjugacy classes.

Findings

Selection rules are governed by automorphisms of discrete groups.

New coupling selection rules depend on conjugacy class labels.

Selection rules can exhibit non-group-like behavior.

Abstract

We clarify selection rules of conjugacy classes of several finite discrete groups where we deal with both gauged and ungauged cases. We find that the selection rules enjoy finite Abelian or non-Abelian discrete symmetries originating from the inner and/or outer automorphism of underlying discrete groups. Since the selection rules of conjugacy classes do not obey conventional group-like selection rules, they open up new coupling selection rules of fields which are labeled by the conjugacy classes.