Decoupling and de Sitter Vacua in Approximate No-Scale Supergravities

TL;DR

This paper investigates how approximate no-scale supergravity models can produce metastable de Sitter vacua, highlighting the conditions for decoupling fields and providing explicit string theory examples with quantized fluxes.

Contribution

It demonstrates that metastable de Sitter vacua in no-scale supergravities require a massless mode besides the no-scale field and provides geometric criteria and explicit solutions in string theory contexts.

Findings

Metastable dS vacua require an additional massless mode in the spectrum.

Decoupling of N-2 fields enables tuning of parameters for metastability.

Explicit dS solutions are constructed in type IIB string theory models, including flux quantization.

Abstract

We study ${\cal N}=1$ supergravity with $N>1$ chiral superfields in which one of the fields has a K\"ahler 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 $N\times N$ 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 ${\cal O}(N^0)$ 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.