Flux moduli stabilisation, supergravity algebras and no-go theorems

Abstract

We perform a complete classification of the flux-induced 12d algebras compatible with the set of N = 1 type II orientifold models that are T-duality invariant, and allowed by the symmetries of the T 6 /(Z 2 ×Z 2 ) isotropic orbifold. The classification is performed in a type IIB frame, where onlyH 3 and Q fluxes are present. We then study no-go theorems, formulated in a type IIA frame, on the existence of Minkowski/de Sitter (Mkw/dS) vacua. By deriving a dictionary between the sources of potential energy in types IIB and IIA, we are able to combine algebra results and no-go theorems. The outcome is a systematic procedure for identifying phenomenologically viable models where Mkw/dS vacua may exist. We present a complete table of the allowed algebras and the viability of their resulting scalar potential, and we point at the models which stand any chance of producing a fully stable vacuum.

Universal dS vacua in STU-models

“…The stable dS in [14][15][16][17] were all found to be close to Mkw vacua with no special properties. The aim of our work is to investigate the existence of examples close to either no-scale or fully supersymmetric Mkw.…”

“…Different theories are specified through various kinds of fluxes due to the metric and gauge fields living on the manifold. In order to find stable dS solution it has turned out to be crucial to turn on non-geometric fluxes, and explicit, successful examples can be found in refs [14][15][16][17].…”

“…In the context of isotropic STU-models, sets of stable dS critical points have been found both with pertubatively [14,16,17] and non-pertubatively [18,19] induced superpotentials. These critical points always turn out to be organised into thin regions in parameter space attached to a line of Mkw solutions.…”

Analytic classes of metastable de Sitter vacua

“…In [4,5] a general strategy of finding dS vacua, that is similar to our own, was proposed and some explicit numerical examples of stable dS vacua in the two-moduli case were discovered. In the simplest supergravity models that might arise in the presence of so-called non-geometric fluxes [6], numerical dS vacua where found in [7][8][9] and more recently in a more complicated model in [10]. 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].…”

De Sitter vacua from a D-term generated racetrack uplift

“…Motivated by this setup, there were many attempts constructing dS vacua [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Using the necessary constraint for the extrema [43,44] and for the stability [45], we see that the existence of minima requires not only negative curvature, but also the presence of orientifold planes.…”