Realizing the bulk-boundary correspondence for anomalous symmetry-enriched topological phases

We construct models of anomalous 2+1D symmetry-enriched topological phases (SETs) on the surfaces of 3+1D symmetry-protected topological phases, providing an explicit realization of the bulk-boundary correspondence for SETs. Our construction takes as input the symmetry fractionalization data and does not require a priori knowledge of the SET’s anomaly. Our method works for both non-permuting and anyon-permuting symmetry actions on both Abelian and non-Abelian topological orders. We discuss the extraction of the absolute anomaly using our construction.