How symmetry defects carry anomalies on their surfaces

When a continuous symmetry has a 't Hooft anomaly, the defects that terminate its topological operators acquire an unavoidable topological dressing — a layer of topological order that reconciles the anomaly inflow. This dressing is not cosmetic: it enforces chiral edge modes on the defect's worldvolume and allows gapless degrees of freedom to be pumped adiabatically by the background flux. The framework is verified explicitly for anomalous chiral symmetries in both continuum field theory and lattice models, connecting abstract anomaly data to concrete physical consequences on defects.