Analytic classes of metastable de Sitter vacua

Abstract

In this paper, we give a systematic procedure for building locally stable dS vacua in N = 1 supergravity models motivated by string theory. We assume that one of the superfields has a Kähler 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 ǫ. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by ǫ 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.

Universal dS vacua in STU-models

“…Unfortunately, as proven in [2], any small deformation of the superpotential (or the Kähler potental) just yields another supersymmetric vacuum -Mkw or AdS. Hence, one can never get a dS in this way.…”

“…Hence, one can never get a dS in this way. The proposed solution of [2] is to add a new field, referred to as a Polonyi field, to generate an additional, flat direction. The Mkw minimum can then be uplifted to a stable dS.…”

“…The Mkw minimum can then be uplifted to a stable dS. Through appropriate choices of parameters, in [2] it is argued that all scalar masses can be made larger than the gravitino mass, and that the cosmological constant can be set at a still much smaller scale.…”

“…This work is inspired by the line of investigation opened up in refs [2,3]. There, the importance of approximate no-scale dS vacua in particular is discussed and a technical machinery is developed for constructing simple analytical families of such solutions.…”

De Sitter vacua from a D-term generated racetrack uplift

“…However, if one stabilizes the complex structure sector at nonsupersymmetric points, then there appears a chance to have a positive contribution in the potential without tachyons, that may be applied for the uplift with a tuning. See also recent applications of this mechanism [17][18][19].…”