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

TL;DR

The paper establishes that bulk 't Hooft anomalies constrain symmetry breaking on defects, forcing anomaly-enforced defect conformal manifolds and enabling anomaly-sensitive observables through modulated defect couplings. By constructing anomalous modulated effective actions via anomaly inflow and Wess-Zumino consistency, it shows universal defect transport phenomena: a Thouless charge pump in (1+1)d and non-dissipative boundary Hall-like responses in higher dimensions. The framework interprets these effects as anomalies in the space of defect couplings and is illustrated with explicit (1+1)d, (2+1)d, and (3+1)d examples, including defect anomalies matched by defect couplings and inflow. The work points to broader avenues, including gravitational/global anomalies, SymTFT approaches for continuous symmetries, and extensions to higher-form or higher-codimension defects.

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.

Figures (6)

• Figure 1: The action of a bulk symmetry operator $U_h$ on a symmetry-breaking defect $D_g$.
• Figure 2: (a) A symmetric defect can be crossed topologically by the bulk symmetry generators via an improvement term. (b) A symmetry-breaking defect is mapped into a modulated defect by a background gauge transformation.
• Figure 3: The Wess–Zumino consistency condition in the presence of a symmetry-breaking defect $D$. Straight defects denote an unmodulated symmetry-breaking, while wiggly ones correspond to modulated defects.
• Figure 4: An upgraded inflow picture including a (modulated) boundary condition. Maintaining bulk topological invariance requires decoration by a $G$-enriched topological action $\gamma(A,g)$. The dynamical physical modes live on the gray area of the figure.
• Figure 5: Half-space RG flow giving rise to a $U(1)_V$-symmetric boundary condition $B_\sigma$ for a single Dirac fermion. This realizes an interface between the massless Dirac fermion and the topological insulator $\nu_\sigma$.