Anomaly Cancellations on Lower-Dimensional Hypersurfaces by Inflow from the Bulk

TL;DR

This paper reviews how anomalies on lower-dimensional hypersurfaces are canceled by inflow from the bulk, with applications in condensed matter physics and M-theory, emphasizing the importance of precise factor and sign treatment.

Contribution

It provides a detailed review of anomaly inflow mechanisms on hypersurfaces, clarifying the factors and signs involved, with applications across physics fields.

Findings

Clarifies the role of topological interactions in anomaly cancellation.

Highlights the importance of factors and signs in anomaly inflow.

Discusses applications in Quantum Hall Effect and M-theory.

Abstract

Lower-dimensional (hyper)surfaces that can carry gauge or gauge/gravitational anomalies occur in many areas of physics: one-plus-one-dimensional boundaries or two-dimensional defect surfaces in condensed matter systems, four-dimensional brane-worlds in higher-dimensional cosmologies or various branes and orbifold planes in string or M-theory. In all cases we may have (quantum) anomalies localized on these hypersurfaces that are only cancelled by ``anomaly inflow'' from certain topological interactions in the bulk. Proper cancellation between these anomaly contributions of different origin requires a careful treatment of factors and signs. We review in some detail how these contributions occur and discuss applications in condensed matter (Quantum Hall Effect) and M-theory (five-branes and orbifold planes)