Anomalies and Symmetry Fractionalization

Understand

We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$.

• In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a fractionalization class, needs to be specified.
• Distinct choices of a fractionalization class can result in different values for the anomalies of $G$ if the theory has an anomaly involving $\Gamma$.
• Therefore, the computation of the 't Hooft anomaly for an ordinary symmetry $G$ generally requires first discovering the one-form symmetry $\Gamma$ of the physical system.