Work

Unitary categorical symmetries

Year: 2026

Type: article

Abstract: Global invertible symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to non-invertible symmetries by considering unitary actions of higher fusion category symmetries C on twisted sector local operators. We propose that the latter transform in ∗ -representations of the tube algebra associated to C , which we introduce and classify using the notion of higher S -matrices of higher braided fusion categories.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ae6be0

Author: Thomas Bartsch

Institution: University of Oxford

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funder: Engineering and Physical Sciences Research Council