Rigid nongeometric orientifolds and the swampland

TL;DR

This paper investigates the potential for realizing de-Sitter solutions in nongeometric flux compactifications within type II string theories, finding significant constraints and no concrete de-Sitter vacua under the studied conditions.

Contribution

It analyzes nongeometric flux compactifications on a specific orientifold, revealing limitations in achieving de-Sitter solutions and identifying a rare case where no-go conditions can be bypassed.

Findings

Type IIB case: Bianchi identities prevent non-zero NS-NS and nongeometric fluxes.

Type IIA case: Most flux solutions lead to no-go de-Sitter scenarios.

Limited numerical search: No de-Sitter vacua found with consistent fluxes.

Abstract

Nongeometric flux compactifications with frozen complex structure moduli have been recently studied for several phenomenological purposes. In this context, we analyze the possibility of realizing de-Sitter solutions in the context of ${\cal N} =1$ type II nongeometric flux compactifications using the ${\mathbb T}^6/({\mathbb Z}_3 \times {\mathbb Z}_3)$ toroidal orientifolds. For the type IIB case, we observe that the Bianchi identities are too strong to simultaneously allow both the NS-NS three-form flux ($H_3$) and the nongeometric ($Q$) flux to take non-zero values, which makes this model irrelevant for phenomenology due to the no-scale structure. For the type IIA case, we find that all the (nongeometric) flux solutions satisfying the Bianchi identities result in de-Sitter no-go scenarios except for one case in which the no-go condition can be evaded. However for this case also, in our (limited) numerical investigation we do not find any de-Sitter vacua using the integer fluxes satisfying all the Bianchi identities.