04.03.2020 (Wednesday)

Global symmetry and anomalies in (2+1)D topological quantum field theories

Triangular Seminar Maissam Barkeshli (University of Maryland)

15:00 QMW
room G.O. Jones LT

Topological quantum field theories, which can be used to model topologically ordered phases of matter in quantum many-body systems, exhibit rich behavior in the presence of global symmetries. In this talk I will present progress over the last few years in understanding (2+1)D TQFTs in the presence of a global symmetry group G. This leads to a new mathematical structure, G-crossed braided tensor categories, that characterizes different possible patterns of symmetry fractionalization for topologically non-trivial particles and the fusion and braiding properties of symmetry defects. Two types of anomalies arise in the discussion: (1) "symmetry localization anomalies," which can also be interpreted as the theory possessing a non-trivial 2-group symmetry, and (2) symmetry fractionalization anomalies, which are equivalent to 't Hooft anomalies of the TQFT. I will describe various methods that have been developed in the past few years to compute these anomalies from the algebraic data that defines the TQFT and the symmetry action.