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(3+1)D topological orders with only a mathbb{Z}₂-charged particle

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arxiv 2011.11165 v1 pith:7HPZZASD submitted 2020-11-23 math.QA cond-mat.str-elhep-thmath.CT

(3+1)D topological orders with only a mathbb{Z}₂-charged particle

classification math.QA cond-mat.str-elhep-thmath.CT
keywords mathbbparticlegaugeonlypuretheorytopologicaldimensional
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 7 Pith papers

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