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

• DOI: 10.1007/s00220-013-1723-0
• Publication Date: 2013-05-09T05:56:50Z
• Authors: Jürgen Fuchs; Christoph Schweigert; Alessandro Valentino
• Keywords: High Energy Physics - Theory; FOS: Physical sciences; Mathematics - Category Theory; 01 natural sciences; High Energy Physics - Theory (hep-th); 0103 physical sciences; FOS: Mathematics; Algebraic Topology (math.AT); Category Theory (math.CT); Mathematics - Algebraic Topology; 0101 mathematics

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.<br/>34 pages, some figures. v2: references added. v3: typos corrected and biliography updated<br/>