Symmetries and defects in three-dimensional topological field theory

Jurgen Fuchs; Christoph Schweigert

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arXiv · 1501.01885

Symmetries and defects in three-dimensional topological field theory

Jurgen Fuchs·Christoph Schweigert

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Abstract

Boundary conditions and defects of any codimension are natural parts of any quantum field theory. Surface defects in three-dimensional topological field theories of Turaev-Reshetikhin type have applications to two-dimensional conformal field theories, in solid state physics and in quantum computing. We explain an obstruction to the existence of surface defects that takes values in a Witt group. We then turn to surface defects in Dijkgraaf-Witten theories and their construction in terms of relative bundles; this allows one to exhibit Brauer-Picard groups as symmetry groups of three-dimensional topological field theories.

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Jurgen Fuchs, Christoph Schweigert. 2015-06-19. Symmetries and defects in three-dimensional topological field theory. https://arxiv.org/abs/1501.01885

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