Global anomalies in M-theory

TL;DR

This paper investigates global anomalies in M-theory on open manifolds and with five-branes, extending previous perturbative anomaly cancellation results to include topological invariants that characterize potential global anomalies.

Contribution

It explicitly constructs topological invariants that detect global anomalies in M-theory configurations involving boundaries and five-branes.

Findings

Global anomalies are characterized by specific topological invariants.

Perturbative anomalies cancel in the considered M-theory setups.

New invariants are identified for detecting global anomalies.

Abstract

We first consider M-theory formulated on an open eleven-dimensional spin-manifold. There is then a potential anomaly under gauge transformations on the E_8 bundle that is defined over the boundary and also under diffeomorphisms of the boundary. We then consider M-theory configurations that include a five-brane. In this case, diffeomorphisms of the eleven-manifold induce diffeomorphisms of the five-brane world-volume and gauge transformations on its normal bundle. These transformations are also potentially anomalous. In both of these cases, it has previously been shown that the perturbative anomalies, i.e. the anomalies under transformations that can be continuously connected to the identity, cancel. We extend this analysis to global anomalies, i.e. anomalies under transformations in other components of the group of gauge transformations and diffeomorphisms. These anomalies are given by certain topological invariants, that we explicitly construct.