By Wehrfritz B.A.F.
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5. There is nothing but the Standard Model with a Higgs boson below the Planck scale. The hierarchy is a mere accident. If the last possibility is not seriously being considered, all conceivable scenarios predict new physics at scales considerably below the Planck scale. , 6 Recently, extra-dimension models have been developed where the solution of the Einstein equations for the background gravitational ﬁeld contains a large exponential factor, thus giving a potential explanation for the hierarchy problem in terms of the fundamental space-time geometry .
When constructing the eﬀective action at higher orders, maintaining unitarity in scattering processes, one has to replace local gauge invariance by a global symmetry, BRS invariance . For the physical ﬁelds, this symmetry coincides with gauge invariance. To make the gauge-ﬁxing term BRS invariant one has to introduce additional ghost ﬁelds and a corresponding interaction term. This setup is necessary for correctly deﬁning interactions at short distances (absorbing UV divergences), but it does not interfere with spontaneous symmetry breaking which is a long-distance phenomenon.
2-Generator conditions in linear groups by Wehrfritz B.A.F.