Non-invertible symmetry enriched string net topological orders
Strongly Correlated Electrons
2026-05-28 v1 Mathematical Physics
Category Theory
math.MP
Quantum Algebra
Quantum Physics
Abstract
We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary fusion categories (UFCs), as well as anyon condensation. In both cases, the NI-SETO is a relative center of UFCs. All NI-SETOs can be realized in either model, where we can use enriched UFCs to get chiral examples on the boundary of a 3D Walker-Wang model representing the anomaly. We describe several examples of NI-SETOs and compute the qualitative symmetry action on anyons and symmetry defects using tube algebra techniques.
Keywords
Cite
@article{arxiv.2605.28794,
title = {Non-invertible symmetry enriched string net topological orders},
author = {Luisa Eck and Peter Huston and Kyle Kawagoe and David Penneys},
journal= {arXiv preprint arXiv:2605.28794},
year = {2026}
}