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$\begingroup$ Kaluza-Klein can be adapted to $\mathrm{U}(1)\times \mathrm{SU}(2)\times \mathrm{SU}(3)$, but the real problem is fermions. One has to use the super-Palatini-MacDowell-Mansouri action and factor the gravitino $\psi_\mu$ into $\gamma_\mu \psi$, for $\psi$ a fermionic field. Then the Higgs mechanism should be introduced via an additional, compact dimension. Really messy, but the resulting action should be quite compact. I am currently working on this in the continuity of my articles, but yeah, things are definitely more complicated. $\endgroup$

Jeanbaptiste Roux
– Jeanbaptiste Roux

2025-05-27 13:22:58 +00:00
Commented May 27 at 13:22

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