Perspectives on Anomaly Resolution

We examine in detail the process of resolving 't Hooft anomalies by extending the symmetry of a theory. Specifically, we interpret the ingredients of existing prescriptions for anomaly resolution as the addition of topological operators with designated mixed anomalies, which can be interpreted as coupling our original field theory to a topological one. We show that, upon gauging, the presence of such mixed anomalies leads to a modified version of the original symmetry which now acts on the newly introduced operators, allowing for an overall anomaly-free action. We also show that the original, anomalous symmetry remains present in the theory. This analysis is applied to anomaly-resolving extensions by both ordinary and higher-form symmetries, leading to related but qualitatively distinct stories.