Frozen up Dilaton and the GUT/Planck Mass Ratio

Abstract

By treating modulus and phase on equal footing, as prescribed by Dirac, local scale invariance can consistently accompany any Brans-Dicke $\omega$-theory. We show that in the presence of a soft scale symmetry breaking term, the classical solution, if it exists, cannot be anything else but general relativistic. The dilaton modulus gets frozen up by the Weyl-Proca vector field, thereby constituting a gravitational quasi-Higgs mechanism. Assigning all grand unified scalars as dilatons, they enjoy Weyl universality, and upon symmetry breaking, the Planck (mass)$^2$ becomes the sum of all their individual (VEV)$^2$s. The emerging GUT/Planck (mass)$^2$ ratio is thus $\sim \omega g_{GUT}^2/4\pi$.