The Derivation of $M_{GUT}=10^{16}GeV$ from A String Model

Abstract

We propose that gaugino condensation in the hidden sector may dynamically induce intermediate gauge symmetry breaking and specify the compactification scale. We also show that this scheme makes possible affine level one grand unified string models with gauge breaking scale $M_{\rm GUT} \sim 10^{16}$ GeV. $T$-duality plays a crucial role in making this scheme possible, even though it is spontaneously broken. We also discuss the generation of the large mass hierarchy between the string scale and the electroweak scale and the solution of the dilaton runaway problem in this scheme.