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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 15th 2009

    created fivebrane 6-group with the idea

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeJan 15th 2022
    If one goes up the Whitehead tower starting from orthogonal group, one passes by the special orthogonal group, the spin group, the string 2-group before finally reaching the fivebrane 6-group. What comes after the fivebrane 6-group?
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 16th 2022
    • (edited Jan 16th 2022)

    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 7S 4S^7 \to S^4, it is natural to speculate that a variant based instead on the octonionic Hopf fibration S 15S 7S^{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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