Symmetries and defects in three-dimensional topological field theory

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.

arXiv commentBased on plenary talks at String Math 2015, Edmonton, and Group 30, Ghent. Some typos corrected

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Cited by in corpus (4)

• Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers
• Extended Functorial Field Theories and Anomalies in Quantum Field Theories
• Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications
• Permutation actions on modular tensor categories of topological multilayer phases