The blog / video (See: https://backreaction.blogspot.com/2021/04/does-universe-have-higher-dimensions.html - Does the Universe have Higher Dimensions? Sabine Hossenfelder's blog) is discussing the history and popular concepts behind Kaluza-Klein approach and its extension to derive and model the other interactions. In that contact, Sabine mention R. Kerner's paper(1968) to extend Kaluza-Klein (to derive any Yang Mills field) and states that it would take +4 additional dimensions to make the strong interaction appear (+1 is the usual KK derivation of EM and +2 for the Weak interaction). Kerner paper or other detailed reviews and work on KK do not mention +4 for the strong interaction. Does anybody have a pointer or a derivation / justification for the +4 (vs. say +3) other than the fact (see below) that at least 7D compact dimensions are required for SM.
Would the dimension result change in a induced space time matter model where the dimensions are not compact (and I am not sure how fiber bundle models are adapted) and 4D spacetime is embedded?
References: Kerner paper: Kerner R 1968, " Generalization of the Kaluza-Klein theory for an arbitrary non-abelian gauge group. " Ann. Inst. H Poincare' 9 143 Other somehow relevant papers: David Bailint and Alex Love, (1987), “Kaluza-Klein theories”, Rep. Prog. Phys. 50 (1987) 1087-1170 https://arxiv.org/abs/1603.03128 Frank Reifler and Randall Morris, "Conditions for exact equivalence of Kaluza-Klein and Yang-Mills theories"
Yes, it is related but not explicitly answered (IMHO) in Does Kaluza-Klein theory successfully unify GR and EM? Why can't it be extended to the Standard Model gauge group?: I am after the explicit generation of the strong interaction. As note in that answer (and in reference above), for SM the minimum dimension is 7. Is it that reasoning that ends up with 4 (vs. 3) for the strong interaction or has an actual derivation been done somewhere.
