Global anomalies in 8d supergravity

TL;DR

This paper classifies gauge and gravitational anomalies in 8-dimensional supergravity, identifying conditions under which anomalies cancel or impose topological restrictions on spacetime manifolds.

Contribution

It determines the spin bordism groups relevant for anomaly classification and analyzes anomaly cancellation mechanisms in 8d supergravity theories.

Findings

Fermions in adjoint representations have anomalies.

Gravitino anomalies are present in 8d supergravity.

Anomaly cancellation involves 2-form fields or topological degrees of freedom.

Abstract

We study gauge and gravitational anomalies of fermions and 2-form fields on eight-dimensional spin manifolds. Possible global gauge anomalies are classified by spin bordism groups $\Omega^{\text{spin}}_9(BG)$ which we determine by spectral sequence techniques, and we also identify their explicit generator manifolds. It turns out that a fermion in the adjoint representation of any simple Lie group, and a gravitino in $8d$ $\mathcal{N}=1$ supergravity theory, have anomalies. We discuss how a 2-form field, which also appears in supergravity, produces anomalies which cancel against these fermion anomalies in a certain class of supergravity theories. In another class of theories, the anomaly of the gravitino is not cancelled by the 2-form field, but by topological degrees of freedom. It gives a restriction on the topology of spacetime manifolds which is not visible at the level of differential-form analysis.