On Unitary 2-Group Symmetries

TL;DR

This paper generalizes the concept of unitary symmetries in quantum systems to extended observables, specifically line operators, using the framework of finite global 2-group symmetries and their 2-representations.

Contribution

It introduces a classification of unitary 2-representations of finite 2-groups acting on line operators, extending known classifications and revealing a reflection anomaly.

Findings

Classified unitary 2-representations of finite 2-groups

Revealed a reflection anomaly in the symmetry action

Extended the understanding of symmetries to line operators

Abstract

Global internal symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to extended observables by considering unitary actions of finite global 2-group symmetries $\mathcal{G}$ on line operators. We propose that the latter transform in unitary 2-representations of $\mathcal{G}$, which we classify up to unitary equivalence. Our results recover the known classification of ordinary 2-representations of finite 2-groups, but provide additional data interpreted as a type of reflection anomaly for $\mathcal{G}$.