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(3+1)D topological orders with only a mathbb{Z}₂-charged particle
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(3+1)D topological orders with only a mathbb{Z}₂-charged particle
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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.
Forward citations
Cited by 7 Pith papers
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A sixteen-fold family of (2+1)D fermionic topological orders is identified, characterized by the mod-16 anomaly of a Z2 one-form symmetry and constructed as gapped boundaries of 3+1D fermionic SPT phases.
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Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
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