Quantum Moduli Spaces of $N=1$ String Theories

TL;DR

This paper explores specific N=1 string models where certain moduli remain unlifted non-perturbatively due to discrete R symmetries, providing insights into moduli stabilization and potential cosmological implications.

Contribution

It identifies models with high-symmetry moduli spaces preserved non-perturbatively, controlled by discrete R symmetries, and computes the associated potential.

Findings

Surviving moduli space is of high symmetry.

Potential computed shows attraction to this subspace.

Implications for dilaton fixing and cosmology.

Abstract

Generically, string models with $N=1$ supersymmetry are not expected to have moduli beyond perturbation theory; stringy non-perturbative effects as well as low energy field-theoretic phenomena such as gluino condensation will lift any flat directions. In this note, we describe models where some subspace of the moduli space survives non-perturbatively. Discrete $R$ symmetries forbid any inherently stringy effects, and dynamical considerations control the field-theoretic effects. The surviving subspace is a space of high symmetry; the system is attracted to this subspace by a potential which we compute. Models of this type may be useful for considerations of duality and raise troubling cosmological questions about string theory. Our considerations also suggest a mechanism for fixing the expectation value of the dilaton.