Strings at the Intermediate Scale, or is the Fermi Scale Dual to the Planck Scale?

Abstract

We show that if the string scale is identifed with the intermediate scale, $M_s=\sqrt{M_W{M}_{Planck}}\sim 10^{11}$ GeV, then the notorious hierarchy, $M_W/M_{Planck}\sim 10^{-16}$, can be explained using only $M_c/M_s\sim 0.01\sim {\alpha }_{GUT}$ as small input parameters, where $M_c$ is the compactification scale. This is possible for weakly-coupled Type-I open-string vacua if the observed world is assumed to live in an N=1 supersymmetric 3-brane sector coupled to a separate, hidden, 3-brane world which breaks supersymmetry, because for such a model $M_W/M_{Planck}=1/2{\alpha }_{GUT}^2(M_c/M_s{)}^6$. We discuss some of the phenomenological issues presented by such an intermediate-scale string, showing that its benefits include: (i) the possibility of logarithmic gauge-coupling unification of the SM couplings at $M_s$; (ii) a natural axionic solution to the strong-CP problem with a phenomenologically-acceptable Peccei-Quinn scale; (iii) experimentally-interesting neutrino masses, and more.

Comments: 16 pages, LaTeX, no figures