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Gapped boundary theories in three dimensions

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arxiv 2006.10200 v3 pith:WZGSK3IM submitted 2020-06-17 math.QA cond-mat.str-elhep-thmath-phmath.ATmath.MP

Daniel S. Freed , Constantin Teleman This is my paper · ORCID
classification math.QAcond-mat.str-elhep-thmath-phmath.ATmath.MP
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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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  1. Discrete quantum systems from topological field theory

    hep-th 2025-06 conditional novelty 8.0 of 10

    A defect-based topological field theory construction yields local gapped lattice Hamiltonians whose ground states reproduce Chern-Simons, toric code, and Levin-Wen models.

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