Moduli potentials in string compactifications with fluxes: mapping the Discretuum

TL;DR

This work analyzes the stabilization of all moduli in 4D $N=1$ SUGRA derived from heterotic and type II string theories, mapping the discretuum of vacua accessible via fluxes and nonperturbative effects to identify stable de Sitter or Minkowski solutions. It examines heterotic moduli potentials with flux, gaugino condensation, threshold corrections, and non-Kähler compactifications, and then reviews type IIB approaches including no-scale structure and racetrack models for Kahler moduli stabilization. A central result is that with a single light modulus, true minima with nonnegative cosmological constant are not achievable via F-terms, whereas two light moduli can yield dS or Minkowski vacua after tuning, with many vacua stabilizing at negative CC or SUSY breaking AdS. The paper also discusses cosmological implications, highlighting the overshoot problem for outer-region vacua and arguing for focusing on central-region moduli to obtain viable cosmologies, while acknowledging the need for nonperturbative understanding and careful tuning within the discretuum.

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.