Constructing de Sitter vacua in no-scale string models without uplifting
  We develop a method for constructing metastable de Sitter vacua in N=1 supergravity models describing the no-scale volume moduli sector of Calabi-Yau string compactifications. We consider both heterotic and orientifold models. Our main guideline is the necessary condition for the existence of metastable vacua coming from the Goldstino multiplet, which constrains the allowed scalar geometries and supersymmetry-breaking directions. In the simplest non-trivial case where the volume is controlled by two moduli, this condition simplifies and turns out to be fully characterised by the intersection numbers of the Calabi-Yau manifold. We analyse this case in detail and show that once the metastability condition is satisfied it is possible to reconstruct in a systematic way the local form of the superpotential that is needed to stabilise all the fields. We apply then this procedure to construct some examples of models where the superpotential takes a realistic form allowed by flux backgrounds and gaugino condensation effects, for which a viable vacuum arises without the need of invoking corrections to the Kahler potential breaking the no-scale property or uplifting terms. We finally discuss the prospects of constructing potentially realistic models along these lines. 
Laura Covi, Marta Gomez-Reino, Christian Gross, Gonzalo A. Palma,   Claudio A. Scrucca