Anomalous Symmetry Fractionalization and surface topological order

Fiona Burnell
University of Minnesota, Twin Cities

I will discuss the relationship between certain symmetry-protected (SPT) phases in 3+1D and problems that can arise in symmetry-enriched topological (SET) phases in 2+1D. Specifically, the difficulty in realizing certain SET phases in 2 spatial dimensions stems from an obstruction to finding a consistent solution to the pentagon equation when the symmetry is gauged. I will focus on the particular example of an anomalous $Z_2 \times Z_2$ symmetry acting projectively on topological excitaitons with semionic statistics, and discuss the origin of the anomaly in the 2D system, and how it is resolved in 3D.

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