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Bicategories for boundary conditions and for surface defects in 3-d TFT · Around

2012

Bicategories for boundary conditions and for surface defects in 3-d TFT

Fuchs, Jurgen, Schweigert, Christoph, Valentino, Alessandro

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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.

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E. Witt,
1937
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S. Mac Lane,
1952
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J. Bénabou,
1967
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G. Moore and N. Seiberg,
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1990
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V.G. Drinfeld,
1990
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N.Yu. Reshetikhin and V.G. Turaev,
1991
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A. Joyal and R. Street,
1993
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G. Delfino, G. Mussardo, and P. Simonetti,
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