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

TL;DR

This paper explores how 't Hooft anomalies influence defect conformal manifolds, revealing topological signatures such as quantized charge pumping and boundary Hall currents in various dimensions.

Contribution

It demonstrates that bulk 't Hooft anomalies enforce defect conformal manifolds and affect their geometric structure through modulated deformations.

Findings

Quantized boundary charge pumping in (1+1)d due to anomalies

Non-dissipative boundary Hall currents in higher dimensions

Anomaly-enforced defect conformal manifolds

Abstract

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.