Global symmetries: locality, unitarity, and regularity

TL;DR

This paper investigates the tension between locality and unitarity in quantum field theory symmetries, introducing an observable to measure non-locality and its relation to fusion algebra data.

Contribution

It proposes a new observable to analyze non-locality in categorical symmetries, linking locality constraints to the fusion algebra structure.

Findings

The observable encodes data related to the fusion algebra of symmetries.

Locality imposes specific regularities on symmetry actions in the Hilbert space.

The approach applies to a class of examples illustrating the non-locality measures.

Abstract

We study the apparent tension between locality and unitarity for symmetries in quantum field theory. This emerges in the context of categorical symmetries where symmetry operators are generically non-invertible. We argue that locality imposes particular regularities in the action of symmetries on the Hilbert space. This allows us to introduce an observable that can measure the properties of the non-locality for symmetry operators. We study it for a class of examples and demonstrate that this observable can encode data associated to the fusion algebra of symmetries.