I would like to interest the PF community in a collective activity based on some topics we have discussed from time to time.(adsbygoogle = window.adsbygoogle || []).push({});

We know that there are seven dimensional manifolds whose isometry group is the same that the standard model gauge group. But they are not enough to get the standard model. Two questions can be raised:

- Why such manifolds are choosen instead the highest symmetric one, the seven-sphere. This is to ask, why the Standard Model gauge group is not SO(8)?

- How to get different representations for left and right spinors, given the non-go theorems of compacification over manifolds?

The guiding idea is that both questions could have a common answer, by finding some orbifold (orientifold?) from a discrete quotient of the seven-sphere. The clue could be the concept of "branched covering", discussed in some papers of Atiyah, that relates CP2 and S4.

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# Can we get the SM from 11D Kaluza Klein?

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