't Hooft Anomalies and Defect Conformal Manifolds: Topological Signatures from Modulated Effective Actions

Symmetry breaking of continuous symmetries by extended dynamical defects entails the existence of defect families, which form conformal manifolds in a critical setup. In the presence of bulk 't Hooft anomalies, defects are in fact required to break the symmetry: defect conformal manifolds are anomaly-enforced. We show that, by coupling the system to a modulated deformation parameter, the geometric structure of the conformal manifold is sensitive to the 't Hooft anomaly. This leads to measurable effects in the presence of a boundary/defect: in (1+1)d the anomaly predicts a quantized boundary charge pumping, while in higher dimensions it gives rise to non-dissipative boundary Hall currents.