3-dimensional defect TQFTs and their tricategories

Abstract

We initiate a systematic study of 3-dimensional `defect' topological quantum field theories, that we introduce as symmetric monoidal functors on stratified and decorated bordisms. For every such functor we construct a tricategory with duals, which is the natural categorification of a pivotal bicategory. This captures the algebraic essence of defect TQFTs, and it gives precise meaning to the fusion of line and surface defects as well as their duality operations. As examples, we discuss how Reshetikhin-Turaev and Turaev-Viro theories embed into our framework, and how they can be extended to defect TQFTs.

60 pages; v2: improved exposition

References in corpus (2)

• Genons, twist defects, and projective non-Abelian braiding statistics
• D-branes and K-theory in 2D topological field theory

Cited by in corpus (24)

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• Line and surface defects in Reshetikhin-Turaev TQFT
• Fermionization of fusion category symmetries in 1+1 dimensions
• Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
• Lecture notes on 2-dimensional defect TQFT
• Orbifolds of Reshetikhin-Turaev TQFTs
• Topological defects
• Domain walls between 3d phases of Reshetikhin-Turaev TQFTs
• Fully extended $\mathbf{r}$-spin TQFTs
• BPS States Meet Generalized Cohomology
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Extended Functorial Field Theories and Anomalies in Quantum Field Theories
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• On 'categories' of quantum field theories
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• Frobenius-Schur Indicators and the Mapping Class Group of the Torus
• Defects in Kitaev models and bicomodule algebras
• Orbifold graph TQFTs
• Orbifold completion of 3-categories
• Truncated affine Rozansky--Witten models as extended defect TQFTs
• A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects