Giving a $KO$ to 8D Gauge Anomalies

TL;DR

This paper constructs an 8D topological field theory that cancels gauge anomalies in 8D gauge theories arising from D-brane configurations, extending the Green-Schwarz mechanism to higher dimensions.

Contribution

It explicitly constructs an 8D TFT using D3-branes and fluxbranes to cancel gauge anomalies in 8D gauge theories with string theory origins.

Findings

Successfully cancels 8D gauge anomalies with the constructed TFT.

Uses topological vector bundles and KO/KSp-homology classes for anomaly cancellation.

Provides a concrete realization of the anomaly inflow mechanism in 8D.

Abstract

In \cite{Garcia-Etxebarria:2017crf}, it was found that the system of $k$ D7-branes probing an $O7^+$-plane suffers from an $\mathfrak{sp}(k)$ gauge anomaly when $k>1$. These authors then conjectured that this 8D $\mathcal{N}=1$ gauge theory couples to an 8D topological field theory (TFT) such that the total system is anomaly-free, thus acting as a "topological" Green-Schwarz mechanism. In this note, we construct such an 8D TFT and show that it indeed cancels the gauge anomaly. The key step is to engineer the relevant topological operators from D3-branes and fluxbranes placed infinitely far away from the stack of 7-branes. Such symmetry operators have topological vector bundles defined on them whose $KO/KSp$-homology classes play a role in the anomaly cancellation.