Abstract
We study \( \mathcal{N} \) = 1 supergravity with N > 1 chiral superfields in which one of the fields has a Kähler potential of exact no-scale type. Such systems admit de Sitter (dS) solutions in which supersymmetry is predominantly broken by the no-scale field, with only a small contribution to the breaking coming from the other fields. Metastable dS vacua of this type were recently shown to be achievable by the finetuning of an N × N sub-matrix of the Hessian matrix at the critical point. We show that perturbatively small deformations of the no-scale Minkowski vacuum into dS are only possible when the spectrum of the no-scale vacuum, besides the no-scale field, contain an additional massless mode. The no-scale structure allows for a decoupling of N −2 fields, and metastability can be achieved by the tuning of \( \mathcal{O}(1) \) parameters. We illustrate this scenario in several examples, and derive a geometric condition for its realisation in type IIB string theory. Supergravities in which the complex structure moduli space is a symmetric space, such as the string theory inspired STU-models, are non-generic and realise a modified version of the scenario. For the STU-model with a single non-perturbative correction we present an explicit analytic family of dS solutions that includes examples with quantised fluxes satisfying the O3-plane tadpole condition.
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Marsh, M.C.D., Vercnocke, B. & Wrase, T. Decoupling and de Sitter vacua in approximate no-scale supergravities. J. High Energ. Phys. 2015, 81 (2015). https://doi.org/10.1007/JHEP05(2015)081
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DOI: https://doi.org/10.1007/JHEP05(2015)081