Bicategories for Boundary Conditions and for Surface Defects in 3-d TFT

By Jürgen Fuchs, Christoph Schweigert, A. Valentino. 2012

211 citations recorded by the source corpus.

We analyze topological boundary conditions and topological surface defects in three-dimensional topological field theories of Reshetikhin-Turaev type based on arbitrary modular tensor categories. Boundary conditions are described by central functors that lift to trivializations in the Witt group of modular tensor categories. The bicategory of boundary conditions can be described through the bicategory of module categories over any such trivialization. A similar description is obtained for topological surface defects. Using string diagrams for bicategories we also establish a precise relation between special symmetric Frobenius algebras and Wilson lines involving special defects. We compare our results with previous work of Kapustin-Saulina and of Kitaev-Kong on boundary conditions and surface defects in abelian Chern-Simons theories and in Turaev-Viro type TFTs, respectively.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/34051d104004f43b6786957ccd9db34d37038c47

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Citations in the corpus

On dualizability of braided tensor categories (2018, background): “tions in the language of braided tensor categories. Many of the algebraic constructions which arise in this unwinding have appeared already in the study of defects in Witten–Reshetikhin–Turaev theory [FSV13], independently of the rigorous (∞,4)-formulation of BrTens but clearly with this motivation ”
Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases (2019, background): “2 It was shown in [21] that the category hom(A,B) along with its action of A actually determines the boundary condition B.”
Higher Gauging and Non-invertible Condensation Defects (2022, methodology): “In the literature, it is also called the symmetric special Frobenius algebra in [7,129] and the -separable Frobenius algebra in [63].”
On the Classification of Topological Orders (2020, result): “[FSV13] Jürgen Fuchs, Christoph Schweigert, and”
Fivebranes and 4-manifolds (2013, background): “or H⊂G. Equivalently, via the level-rank – 34 – or, in the supersymmetric context, Giveon-Kutasov duality [71] equally important are levelchanging defect walls in N= 2 Chern-Simons theories. See e.g. [70] for the study of defect walls with these properties in a purely bosonic theory and [72,73] for ”