The Local Structure of Anomaly Inflow
Jeffrey A. Harvey, Oleg Ruchayskiy
TL;DR
This paper investigates the local structure of anomaly inflow by analyzing a 3+1D axion-string model, revealing that the so-called bump-form responsible for anomaly cancellation originates from the radial profile of fermion zero modes bound to the defect. By computing the zero-mode current and matching its gauge variation to the bulk effective action, the authors derive a explicit relation ρ(r) = (1/2π) ∫_0^r σ F^2(σ)dσ, showing that the bump-form is fixed by the zero-mode wavefunction rather than the defect profile itself. The work clarifies the distinction between covariant and consistent anomalies in inflow and discusses how these insights generalize to M-theory fivebranes, including how the bump-form would appear in the modified Bianchi identity for G_4 and in Chern-Simons couplings. While the axion-string example is not fully representative of the M5-brane case, the results provide a physical interpretation for the smoothing mechanism and a concrete route to derive bulk modifications from near-defect degrees of freedom.
Abstract
Anomaly cancellation for M-theory fivebranes requires the introduction of a "bump-form" which smoothes out the five-brane source. We discuss the physical origin of this bump-form in the simpler case of axion strings in 3+1 dimensions and construct it in terms of the radial profile of the fermion zero modes. Our treatment allows for a clearer understanding of the role played by covariant rather than consistent anomalies when anomalies are canceled by inflow from the bulk. We briefly discuss the generalization of these results to fivebrane anomalies in M theory.