Couplings and Scales in Strongly Coupled Heterotic String Theory

Abstract

If nature is described by string theory, and if the compactification radius is large (as suggested by the unification of couplings), then the theory is in a regime best described by the low energy limit of $M$-theory. We discuss some phenomenological aspects of this view. The scale at which conventional quantum field theory breaks down is of order the unification scale and consequently (approximate) discrete symmetries are essential to prevent proton decay. There are one or more light axions, one of which solves the strong CP problem. Modular cosmology is still problematic but much more complex than in perturbative string vacua. We also consider a range of more theoretical issues, focusing particularly on the question of stabilizing the moduli. We give a simple, weak coupling derivation of Witten's expression for the dependence of the coupling constants on the eleven dimensional radius. We discuss the criteria for the validity of the long wavelength analysis and find that the "real world" seems to sit just where this analysis is breaking down. On the other hand, residual constraints from N=2 supersymmetry make it difficult to see how the moduli can be stabilized while at the same time yielding a large hierarchy.