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arXiv · 2006.10200

Gapped boundary theories in three dimensions

Daniel S. Freed·Constantin Teleman
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Abstract

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. 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 and on internal duals may be of independent interest.; v2 extensive revision: added theorem on dualizable 2-categories, material on natural transformations, reworked theorems and several proofs, and more.

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Daniel S. Freed, Constantin Teleman. 2020-06-17. Gapped boundary theories in three dimensions. https://doi.org/10.1007/s00220-021-04192-x

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