Remarks on the racetrack scheme: Stabilizing the moduli of string theory

There are only a small number of ideas for stabilizing the moduli of string theory. One of the most appealing of these is the racetrack mechanism, in which a delicate interplay between two strongly interacting gauge groups fixes the value of the coupling constant. In this paper, we explore this scenario. We find that, quite generally, some number of discrete tunings are required in order that the mechanism yield a small gauge coupling. Even then, there is, in general, no systematic weak coupling approximation. On the other hand, certain holomorphic quantities can be computed, so such a scheme is in principle predictive. Searching for models which realize this mechanism is thus of great interest. We also remark on cosmology in these schemes.