Gapped Boundary Theories in Three Dimensions
Gapped Boundary Theories in Three Dimensions
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DOI：
10.1007/s00220-021-04192-x
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发表时间：
2020-06
影响因子：
2.4
通讯作者：
D. Freed;C. Teleman
中科院分区：
文献类型：
--
作者：
D. Freed;C. Teleman
本文证明了三维拓扑场论中的一个定理：Reshetikhin-Turaev理论存在非零边界理论当且仅当它是Turaev-Viro理论.这个证明直接暗示了融合范畴在对偶性方面的一个特征。我们的结果依赖于一个（特殊情况下）的协边假设与奇点。主要定理适用于物理学，它意味着一个障碍，以间隙三维量子系统承认间隙边界理论。关于边界主义多范畴、关于2-可对偶范畴和关于内部可对偶范畴的附录可能具有独立的意义。
We prove a theorem in 3-dimensional topological field theory: a Reshetikhin–Turaev theory admits a nonzero boundary theory iff it is a Turaev–Viro theory. The proof immediately implies a characterization of fusion categories in terms of dualizability. Our results rely on a (special case of) the cobordism hypothesis with singularities. The main theorem applies to physics, where it implies an obstruction to a gapped 3-dimensional quantum system admitting a gapped boundary theory. Appendices on bordism multicategories, on 2-dualizable categories, and on internal duals may be of independent interest.