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arXiv · 2203.12631

Global anomalies in 8d supergravity

Yasunori Lee·Kazuya Yonekura
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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.

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Yasunori Lee, Kazuya Yonekura. 2022-03-23. Global anomalies in 8d supergravity. https://doi.org/10.1007/jhep07(2022)125

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