Remarks on the Racetrack Scheme
Michael Dine, Yuri Shirman
TL;DR
The paper analyzes the Racetrack Scheme as a mechanism to stabilize string/M-theory moduli in a way that yields small, unified gauge couplings. It distinguishes SUSY-conserving and SUSY-breaking realizations, showing that holomorphic quantities such as the superpotential and gauge coupling functions can be computed under certain conditions, but nonholomorphic elements like the Kähler potential introduce large uncertainties and potential noncalculability. Achieving a weak coupling regime generally requires discrete fine-tuning (e.g., near-degenerate beta functions or discrete R-symmetries), and the viability of the approach hinges on the underlying string theory limit and SUSY-breaking scale. The authors discuss cosmological implications, the prospects for inflation, and how the racetrack compares to alternative stabilization scenarios, arguing that while attractive and concrete, the scheme faces significant calculability caveats and calls for explicit string constructions.
Abstract
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 note, 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 no sense in which a weak coupling approximation is valid. 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.