# 8d gauge anomalies and the topological Green-Schwarz mechanism

Journal of High Energy Physics, Nov 2017

String theory provides us with 8d supersymmetric gauge theory with gauge algebras $\mathfrak{s}\mathfrak{u}(N),\mathfrak{s}\mathfrak{o}(2N),\mathfrak{s}\mathfrak{p}(N),{\mathfrak{e}}_6,{\mathfrak{e}}_7\kern0.5em \mathrm{and}\kern0.5em {\mathfrak{e}}_8$, but no construction for $\mathfrak{so}\left(2N+1\right)$, ${\mathfrak{f}}_4$ and ${\mathfrak{g}}_2$ is known. In this paper, we show that the theories for ${\mathfrak{f}}_4$ and $\mathfrak{so}\left(2N+1\right)$ have a global gauge anomaly associated to π d=8, while ${\mathfrak{g}}_2$ does not have it. We argue that the anomaly associated to π d in d-dimensional gauge theories cannot be canceled by topological degrees of freedom in general. We also show that the theories for $\mathfrak{s}\mathfrak{p}(N)$ have a subtler gauge anomaly, which we suggest should be canceled by a topological analogue of the Green-Schwarz mechanism.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP11%282017%29177.pdf

Iñaki García-Etxebarria, Hirotaka Hayashi, Kantaro Ohmori, Yuji Tachikawa, Kazuya Yonekura. 8d gauge anomalies and the topological Green-Schwarz mechanism, Journal of High Energy Physics, 2017, 177, DOI: 10.1007/JHEP11(2017)177