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created fivebrane 6-group with the idea
By dimensional reasons it’s natural to speculate that killing the next non-torsion homotopy group gives “ninebrane structure” (Sati: arXiv:1405.7686). But there remains little known for sure on the physics side about the would-be nine-brane that one can compare the resulting structure to.
To some extent this problem was already the case for the fivebrane structures. Just to note in this case that – under “Hypothesis H” – we gave a rigorous proof that fivebrane structure cancels an M5-brane anomaly: see Ex. 3.2 and Rem. 4.3 in “Twisted Cohomotopy implies M5 WZ term level quantization”.
Since this discussion ultimately rests all on the quaternionic Hopf fibration $S^7 \to S^4$, it is natural to speculate that a variant based instead on the octonionic Hopf fibration $S^{15} \to S^7$ would give an analogous rigorous statement about 9-brane structure. But this would remain to be worked out.
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