Topological Orders in (4+1)-Dimensions

Abstract

We investigate the Morita equivalences of (4+1)-dimensional topological orders. We show that any (4+1)-dimensional super (fermionic) topological order admits a gapped boundary condition -- in other words, all (4+1)-dimensional super topological orders are Morita trivial. As a result, there are no inherently gapless super (3+1)-dimensional theories. On the other hand, we show that there are infinitely many algebraically Morita-inequivalent bosonic (4+1)-dimensional topological orders.

arXiv comment18 pages, 2 figures

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• Fusion 3-Categories for Duality Defects
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• Non-Abelian Self-Correcting Quantum Memory and Transversal Non-Clifford Gate beyond the $n^{1/3}$ Distance Barrier