论文标题
（3+1）D只有$ \ mathbb {z} _2 $ - 带电粒子的拓扑订单
(3+1)D topological orders with only a $\mathbb{Z}_2$-charged particle
论文作者
论文摘要
恰好有一个骨（3+1） - 维拓扑顺序，其唯一的非平凡粒子是一个新兴的玻色子：纯$ \ mathbb {z} _2 $ gauge理论。恰好有两个（3+1） - 维拓扑顺序，其唯一的非平凡粒子是一个新兴的fermion：纯“自旋 - $ \ mathbb {z} _2 _2 $”量规理论，其中动态场是旋转结构；以及其异常版本。我给出了此分类的三个证据，从动手到抽象不等。一路上，我提供了纯旋转中的纯字符串和粒子运算符的编织融合$ 2 $ -2 $ - 类别$ \ mathcal {z} _ {（1）}（σ\ Mathbf {svec}）$。
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 $\mathcal{Z}_{(1)}(Σ\mathbf{SVec})$ of string and particle operators in pure spin-$\mathbb{Z}_2$ gauge theory.
