Flux Compactifications, Gauge Algebras and De Sitter

TL;DR

The paper investigates whether flux compactifications in ${\cal N}=4$ gauged supergravity can realize De Sitter vacua by mapping fluxes (including non-geometric ones) to the four-dimensional gauge algebra via the embedding-tensor formalism. It analyzes the resulting algebras in various dual frames, highlighting that the physically consistent IIB/O3-frame flux algebra is non-semi-simple due to an Abelian ideal, which cannot reproduce the known De Sitter gaugings that require direct-product semisimple factors. Consequently, De Sitter solutions do not arise from these ${\cal N}=4$ flux compactifications within the analyzed framework, implying no higher-dimensional geometric or non-geometric origin for such vacua in this setting. The authors discuss potential routes to circumvent the no-go, such as moving to ${\cal N}=1$ constructions or exploring more general fluxes and embeddings that could yield semisimple gaugings.

Abstract

The introduction of (non-)geometric fluxes allows for N=1 moduli stabilisation in a De Sitter vacuum. The aim of this letter is to assess to what extent this is true in N=4 compactifications. First we identify the correct gauge algebra in terms of gauge and (non-)geometric fluxes. We then show that this algebra does not lead to any of the known gaugings with De Sitter solutions. In particular, the gaugings that one obtains from flux compactifications involve non-semi-simple algebras, while the known gaugings with De Sitter solutions consist of direct products of (semi-)simple algebras.