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

Abstract

We propose that a modified version of string-inspired supersymmetry breaking schemes in \cite{wit2} and \cite{ross} may make affine level one SU(5) and SO(10) string models with intermediate gauge symmetry breaking scale $M_{GUT}=10^{16}GeV$ possible; doublet-triplet problem can also be solved. In particular, we propose that some charged gauge background VEVs might be turned on when gaugino condensation happens in the hidden sector and would break gauge symmetry. One can dynamically determine gaugino condensation scale, local supersymmetry breaking scale and intermediate gauge symmetry breaking scale $M_{GUT}$ in terms of dilaton VEV. With dilaton VEV, $\langle S \rangle \sim 2$, and $E_6$ hidden sector gaugino condensation, we can obtain $M_{GUT}=10^{16}GeV$. We also discuss how to generate the mass hierarchy within the framework of this supersymmetry breaking scheme. We show that the large mass hierarchy restricts string models to those that have a no-scale structure and in which the gauge coupling function does not receive string threshold corrections.