What bordism-theoretic anomaly cancellation can do for U

Abstract

We perform a bordism computation to show that the $E_{7(7)}(\mathbb{R})$ U-duality symmetry of 4d $\mathcal{N}=8$ supergravity could have an anomaly invisible to perturbative methods; then we show that this anomaly is trivial. We compute the relevant bordism group using the Adams and Atiyah-Hirzebruch spectral sequences, and we show the anomaly vanishes by computing $\eta$-invariants on the Wu manifold, which generates the bordism group.

29 pages, 4 figures

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Cited by in corpus (4)

• The Smith Fiber Sequence and Invertible Field Theories
• Bosonization and Anomaly Indicators of (2+1)-D Fermionic Topological Orders
• Cancelling mod-2 anomalies by Green-Schwarz mechanism with $B_{\mu \nu }$
• Smith homomorphisms and Spin${}^h$ structures