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 $\epsilon$. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by $\epsilon$ 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.
Highlights
The uplifting energy and the value of the AdS minimum can take many different values, including very small ones, which allows for an anthropic explanation of the observed value of Λ in the context of the string theory landscape
In this paper, we give a systematic procedure for building locally stable dS vacua in N = 1 supergravity models motivated by string theory
Other interesting ways to construct de Sitter vacua using a single step mechanism in string theory motivated N = 1 supergravity models have been suggested over the years, for example in [11,12,13,14,15,16,17,18,19,20]
Summary
For models where the components of Vab can be made suitably small This ensures positive-definiteness of the full mass matrix. They are relatively easy to find, see for example [24] They have a non-negative definite mass matrix of the form (2.6), since a supersymmetric Minkowski vacuum has W = 0 and Fa = 0 and Vab = 0 (cf (2.3)). It follows from (2.4) for SUSY Minkowski vacua that Vab = |D2W |2ab and it is positive-definite. Using the hierarchy (2.8), we establish that there is a large region of Λ and ǫ parameter space where the entire diagonal block of the mass matrix Vab is positive definite. The mass matrix is of the form (2.6) and the local stability of abundant dS solutions is guaranteed by the conditions (2.9), (2.10)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
