Global anomalies in 8d supergravity

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(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 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.

Automated summary

In this paper, we study the gauge and gravitational anomalies of fermions and 2-form fields on eight-dimensional spin manifolds. By using spectral sequence techniques, we classify possible global gauge anomalies and identify their explicit generator manifolds. It is found that fermions in the adjoint representation of any simple Lie group and gravitinos in 8d N = 1 supergravity theory have anomalies. We also discuss how the anomalies of 2-form fields cancel against the fermion anomalies in certain supergravity theories, as well as how the gravitino anomalies are canceled by topological degrees of freedom in another class of theories.