Abstract
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 πd=8, while \( {\mathfrak{g}}_2 \) does not have it. We argue that the anomaly associated to πd 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.
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García-Etxebarria, I., Hayashi, H., Ohmori, K. et al. 8d gauge anomalies and the topological Green-Schwarz mechanism. J. High Energ. Phys. 2017, 177 (2017). https://doi.org/10.1007/JHEP11(2017)177
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DOI: https://doi.org/10.1007/JHEP11(2017)177