Rutgers University Department of Physics and Astronomy
Video File

Maissam Barkeshli
(University of Maryland)

Symmetry fractionalization, defects, and anomalies in (2+1) dimensional topological quantum matter

Abstract: 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. Recently, it has been understood how such symmetry-enriched topological phases of matter can be described by an algebraic framework known as a G-crossed braided tensor category. I will describe this theory and how it provides a way to characterize symmetry fractionalization, the properties of symmetry defects, and even discover the appearance of non-trivial 2-group symmetries when applicable. By studying consistency of the properties of the symmetry defects, this theory can also be used to explicitly compute global anomalies. The anomalies can be computed in general for all symmetry types, including discrete and/or space-time orientation-reversing symmetries, and without the need for a Lagrangian description of the theory.

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