In topological phases with symmetry, the fractional excitations in the system can transform under symmetry in a fractional way, e.g. carrying fractional symmetry charges. It is known that some of these symmetry enriched topological (SET) phases can only be realized on the surface of a system in one higher dimension and various methods have been derived to identify such anomalous SETs in 2+1D. However, not much is known about 3+1D SETs. In this talk, I will discuss a simple anomaly detection method which can be easily generalized to 3+1D. The basic idea is to thread symmetry fluxes into the system and study how the symmetry fractionalizes on the fluxes. Anomaly is detected when the symmetry fractionalization pattern on the fluxes is not consistent with that on the fractional excitations. In particular, we are going to apply this method to demonstrate the anomaly in a 2+1D Z2 gauge theory with U(1)xT symmetry and a 3+1D Z2 gauge theory with U(1)xZ2 symmetry.
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