Standard Model Gauge Couplings from Gauge-Dilatation Symmetry Breaking

Abstract

We argue that there is a spontaneously broken rotational symmetry between space-time coordinates and gauge theoretical phases. The dilatonic mode acts as the massive Higgs boson, whose vacuum expectation value determines the gauge couplings. This mechanism requires that the quadratic divergences, or tadpoles of the three gauge-theory couplings, unify at a certain scale. We verify this statement, and find that this occurs at \Lambda_u ~ 4x10^7 GeV. The tadpole cancellation condition, together with the dilaton self-energy, fixes the value of the unified tadpole coefficient to be 1/[4 ln(\Lambda_cut/\Lambda_u)]. The observed values of the coupling constants at \Lambda_u then implies \Lambda_cut ~ 4x10^18 GeV, which is close to the value of the reduced Planck mass MR_Pl=M_Pl/sqrt(8 pi)=2.4 x 10^18 GeV. In other words, by assuming a cutoff at M_Pl or MR_Pl, we are able to obtain predictions for the gauge couplings which agree with the true values to within a few percent. It turns out that this symmetry breaking can only take place if mass is generated with the aid of some other means such as electroweak symmetry breaking. Assuming dynamical symmetry breaking originating at MR_Pl, we obtain M_chi ~ 10^9 GeV, which is not unreasonable but somewhat higher than \Lambda_u. The cancellation of an anomaly in the dilaton self-energy requires that the number of fermionic generations equals three.