Global gravitational anomaly cancellation for five-branes

TL;DR

The work proves that the global mixed gauge-gravitational anomaly on the M5-brane worldvolume cancels when bulk inflow from the M-theory Chern-Simons term is included, and extends this result to Type IIA and heterotic $E_8\times E_8$ five-branes. It introduces a precise differential cocycle framework to define the M5-brane C-field restriction $\check{C}_M$ and a consistent coupling to the self-dual field via the Wu class, while also formulating the chiral fermions on non-spin worldvolumes. The analysis combines chiral-fermion eta-invariants, the global anomaly of the self-dual field, and the Chern-Simons inflow to show complete cancellation, modulo a cobordism obstruction $\Omega^{M5}_{12}$ that vanishes modulo torsion. This result strengthens the consistency of M-theory backgrounds with five-branes and extends naturally to NS5-branes in Type IIA and heterotic strings, refining the role of differential cohomology and Wu-class shifts in higher-dimensional anomaly physics.

Abstract

We show that the global mixed gauge-gravitational anomaly of the worldvolume theory of the M5-brane vanishes, when the anomaly inflow from the bulk is taken into account. This result extends to the type IIA and heterotic $E_8 \times E_8$ five-branes. As a by-product, we provide a definition of the chiral fermionic fields for generic non-spin M5-brane worldvolume and determine the coupling between the self-dual field and the M-theory C-field.