Strings at the intermediate scale or is the Fermi scale dual to the Planck scale?

Abstract

We show that if the string scale is identified with the intermediate scale, M s= M WM Planck ∼10 11 GeV, then the notorious hierarchy, M W / M Planck∼10 −16, can be explained using only M c / M s ∼0.01∼ α 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 α 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.