Moduli potentials in string compactifications with fluxes: mapping the Discretuum

TL;DR

This paper demonstrates the existence of de Sitter and flat space solutions with stabilized moduli in string compactifications, highlighting the conditions for tuning parameters to achieve large volume, weak coupling, and controlled approximations.

Contribution

It provides a framework for finding stable de Sitter and flat vacua in string theory with all moduli stabilized, addressing previous obstacles and discussing the role of anthropic reasoning.

Findings

Stable de Sitter and flat vacua with all moduli stabilized are achievable.

Large volume and weak coupling regimes can be realized through parameter tuning.

Most stable vacua are likely in the non-perturbative central region of moduli space.

Abstract

We find de Sitter and flat space solutions with all moduli stabilized in four dimensional supergravity theories derived from the heterotic and type II string theories, and explain how all the previously known obstacles to finding such solutions can be removed. Further, we argue that if the compact manifold allows a large enough space of discrete topological choices then it is possible to tune the parameters of the four dimensional supergravity such that a hierarchy is created and the solutions lie in the outer region of moduli space in which the compact volume is large in string units, the string coupling is weak, and string perturbation theory is valid. We show that at least two light chiral superfields are required for this scenario to work, however, one field is sufficient to obtain a minimum with an acceptably small and negative cosmological constant. We discuss cosmological issues of the scenario and the possible role of anthropic considerations in choosing the vacuum of the theory. We conclude that the most likely stable vacuua are in or near the central region of moduli space where string perturbation theory is not strictly valid, and that anthropic considerations cannot help much in choosing a vacuum.