Reshetikhin–Turaev theories are fully local

Abstract: I will review two results pertaining to 3-dimensional Reshetikhin–Turaev TQFTs, defined from modular tensor categories M. These theories were not constructed as “fully local” TQFTs (in the framework of Lurie’s Cobordism Hypothesis): no algebraic structures were assigned to points. (The obstruction was the Witt class of M.) Kevin Walker solved the locality problem in the setting of anomalous theories. A ‘no-go’ theorem (joint with Dan Freed) showed that, if localized as linear theories, these RT theories did not admit local topological boundary conditions, and could therefore not be generated from a point by this method. (The group-like case had been addressed by Kapustin and Saulina.) In recent work with Freed and Claudia Scheimbauer, we displayed a fully local realization of these theories, by objects in a target 3-category which enlarges that of fusion categories. This allowed us to settle some conjectures relating orientations and spherical structures.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

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