Remarks on the Racetrack Scheme

TL;DR

This paper examines the racetrack mechanism in string theory for stabilizing moduli, highlighting the need for fine-tuning and discussing its implications for weak coupling and cosmology.

Contribution

It analyzes the conditions and limitations of the racetrack scheme, emphasizing the necessity of discrete tunings and its potential for predictive calculations.

Findings

Discrete tunings are generally required for small gauge couplings.

Weak coupling approximation is not valid in typical racetrack scenarios.

Certain holomorphic quantities remain computable, allowing for some predictability.

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.