Precision prediction of gauge couplings and the profile of a string theory

Abstract

We estimate the significance of the prediction for the gauge couplings in the MSSM with an underlying unification. The correlation between the couplings covers only (0.2-2)% of the a priori reasonable region of the parameter space, while the prediction for $\sin ^{2}θ_{W}$ is accurate to 1.3%. Given that agreement with experiment to such precision is unlikely to be fortuitous, we discuss the profile of a string theory capable of preserving this level of accuracy. We argue that models with a low scale of unification involving power law running in the gauge couplings do not. Even theories with a high scale of unification are strongly constrained, requiring the compactification scale of new space dimensions in which states transforming under the Standard Model propagate to be very close to the string cut-off scale. As a result {\it no} new space dimensions can be larger than $10^{-14}fm.$