Anomalies in bosonic SPT edge theories: connection to F-symbols and a method for calculation

Understand

We describe a systematic procedure for determining the identity of a 2D bosonic symmetry protected topological (SPT) phase from the properties of its edge excitations.

• Our approach applies to general bosonic SPT phases with either unitary or antiunitary symmetries, and with either continuous or discrete symmetry groups, with the only restriction being that the symmetries must be on-site.
• Concretely, our procedure takes a bosonic SPT edge theory as input, and produces an element $\omega$ of the cohomology group $H^3(G, U_T(1))$.
• This element $\omega \in H^3(G, U_T(1))$ can be interpreted as either a label for the bulk 2D SPT phase or a label for the anomaly carried by the SPT edge theory.