Communications in Mathematical Physics

, Volume 321, Issue 2, pp 543–575 | Cite as

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

  • Jürgen Fuchs
  • Christoph SchweigertEmail author
  • Alessandro Valentino


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.


Wilson Line Module Category Monoidal Category Tensor Category Fusion Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jürgen Fuchs
    • 1
  • Christoph Schweigert
    • 2
    Email author
  • Alessandro Valentino
    • 2
  1. 1.Teoretisk fysikKarlstads UniversitetKarlstadSweden
  2. 2.Fachbereich MathematikUniversität Hamburg, Bereich Algebra und ZahlentheorieHamburgGermany

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