Realizing Braided Fusion 2-Categories as (3+1)D Mixed-State Topological Orders
Abstract
We construct large families of mixed-state topological orders in (3+1)D, including intrinsically mixed-state topological orders. We realize these theories by relating the data parameterizing braided fusion 2-categories to the strong higher-form symmetries and their anomalies that characterize mixed-state topological order. We focus here on bosonic theories, which include theories which admit an emergent fermion in the spectrum of line operators. Our general framework is exemplified on the lattice, where we present concrete models and identify how the data of braided fusion 2-categories are physically encoded. We then formalize this data and show that every braided fusion 2-category arises from a general construction (decoherence followed by strong and weak gauging) as the category of topological operators of a (3+1)D mixed state, with intrinsically mixed-state topological orders distinguished by the presence of strong higher-form symmetries whose anomalies cannot be realized in any (3+1)D gapped ground state. Notably, we show that (3+1)D admits a new mechanism with no (2+1)D counterpart: intrinsically mixed-state order whose topological operators braid non-degenerately, but which carries a gravitational anomaly.
Related
- Property F and weak integrality of braided fusion categories
- An Ito-Michler type theorem and the prime class graph of weakly integral braided fusion categories
- The Galois actions on braided fusion categories
- G-crossed braided tensor categories of twisted modules
- Frobenius functors and one-sided Hopf algebras in braided monoidal categories
BibTeX
@misc{kobayashi2026realizing,
title = {{Realizing Braided Fusion 2-Categories as (3+1)D Mixed-State Topological Orders}},
author = {Ryohei Kobayashi and Abhinav Prem and Matthew Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03864},
eprint = {2610.03864},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03864},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Realizing Braided Fusion 2-Categories as (3+1)D Mixed-State Topological Orders
AU - Ryohei Kobayashi
AU - Abhinav Prem
AU - Matthew Yu
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03864
UR - https://arxiv.org/abs/2610.03864
AB - We construct large families of mixed-state topological orders in (3+1)D, including intrinsically mixed-state topological orders. We realize these theories by relating the data parameterizing braided fusion 2-categories to the strong higher-form symmetries and their anomalies that characterize mixed-state topological order. We focus here on bosonic theories, which include theories which admit an emergent fermion in the spectrum of line operators. Our general framework is exemplified on the lattice, where we present concrete models and identify how the data of braided fusion 2-categories are physically encoded. We then formalize this data and show that every braided fusion 2-category arises from a general construction (decoherence followed by strong and weak gauging) as the category of topological operators of a (3+1)D mixed state, with intrinsically mixed-state topological orders distinguished by the presence of strong higher-form symmetries whose anomalies cannot be realized in any (3+1)D gapped ground state. Notably, we show that (3+1)D admits a new mechanism with no (2+1)D counterpart: intrinsically mixed-state order whose topological operators braid non-degenerately, but which carries a gravitational anomaly.
ER -