(3+1)D topological orders with only a ${\mathbb{Z}}_2$-charged particle

Abstract

There is exactly one bosonic (3+1)-dimensional topological order whose only nontrivial particle is an emergent boson: pure ${\mathbb{Z}}_2$ gauge theory. There are exactly two (3+1)-dimensional topological orders whose only nontrivial particle is an emergent fermion: pure "spin-${\mathbb{Z}}_2$" gauge theory, in which the dynamical field is a spin structure; and an anomalous version thereof. I give three proofs of this classification, varying from hands-on to abstract. Along the way, I provide a detailed study of the braided fusion $2$-category ${\mathcal{Z}}_{(1)}(\Sigma \mathbf{SVec})$ of string and particle operators in pure spin-${\mathbb{Z}}_2$ gauge theory.

arXiv comment30 pages

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Cited by in corpus (8)

• On lattice models of gapped phases with fusion category symmetries
• Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Non-invertible topological defects in 4-dimensional ${\mathbb{Z}}_2$ pure lattice gauge theory
• On the Dualizability of Fusion 2-Categories
• Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd)
• Knots and entanglement
• Loops in 4+1d Topological Phases