Analytic Classes of Metastable de Sitter Vacua

TL;DR

The authors address the challenge of realizing metastable de Sitter vacua in string-motivated $\mathcal{N}=1$ supergravity by exploiting a no-scale modulus and a hierarchical SUSY-breaking pattern controlled by $\\epsilon$ and $\\Lambda$. They develop a systematic analytic procedure: ensure a positive-definite diagonal mass block $V_{a\bar{b}}$, suppress off-diagonal blocks $V_{ab}$ via tuning higher-derivative data in the superpotential $W$, and solve for $\\Lambda$ and $\\epsilon$ to obtain abundant locally stable vacua; they illustrate the method with explicit STU-model solutions and classify vacua into two classes depending on the status of $V_{ab}$. A no-go theorem shows that infinitesimal deformations of a SUSY Minkowski vacuum with no flat directions cannot yield a non-supersymmetric vacuum, motivating alternative uplift strategies. The paper further develops F-term uplifting using KL-type racetrack or Polonyi fields, yielding stable dS vacua with tunable, typically small, gravitino masses, and discusses the embedding and generalization to broader string compactifications beyond the STU setup.

Abstract

In this paper, we give a systematic procedure for building locally stable dS vacua in $\mathcal{N}=1$ supergravity models motivated by string theory. We assume that one of the superfields has a Kahler potential of no-scale type and impose a hierarchy of supersymmetry breaking conditions. In the no-scale modulus direction the supersymmetry breaking is not small, in all other directions it is of order $ε$. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by $ε$ and the cosmological constant. These regions exist regardless of the details of the other moduli, provided the superpotential can be tuned such that the off-diagonal blocks of the mass matrix are parametrically small. We test and support this general dS landscape construction by explicit analytic solutions for the STU model. The Minkowski limits of these dS vacua either break supersymmetry or have flat directions in agreement with a no-go theorem that we prove, stating that a supersymmetric Minkowski vacuum without flat directions cannot be continuously deformed into a non-supersymmetric vacuum. We also describe a method for finding a broad class of stable supersymmetric Minkowski vacua that can be F-term uplifted to dS vacua and which have an easily controllable SUSY breaking scale.