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arXiv · 2011.11165

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

Theo Johnson-Freyd
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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.

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BibTeXRIS

Theo Johnson-Freyd. 2020-11-23. (3+1)D topological orders with only a $\mathbb{Z}_2$-charged particle. https://arxiv.org/abs/2011.11165

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