Taxonomy of type II orientifold flux vacua in 3D

TL;DR

Arboleya, Casagrande, Guarino, and Morittu systematically classify 3D flux vacua from type II orientifold reductions on twisted seven-tori with a single O$p$-plane, restricting to SO$(3)$-invariant RSTU-models and vanishing axions. They exhaustively construct 56 inequivalent flux-vacua families (AdS$_{3}$ and Mkw$_{3}$) plus one trivial vacuum, all within Type IIB frames with O9/O5/O3; among these, only two AdS$_{3}$ vacua in the O5 frame stabilise all dilaton-like moduli and exhibit scale separation, while O9 frames fail to stabilize the internal volume and O3 frames yield only Mkw$_{3}$ vacua with diverse SUSY breaking. Type IIA vacua do not add new physics beyond T-dual IIB ones, with a small set of AdS$_{3}$ vacua in the O6 frame and no new O4/O7 realizations; some vacua allow partial or full supersymmetry enhancements at special flux values. The work discusses moduli stabilization and the prospect of achieving a weakly coupled, scale-separated regime (potentially via non-perturbative effects to fix remaining moduli), highlighting the rarity of such vacua in this setup. Overall, the results map the landscape of 3D flux vacua in RSTU-models and clarify the role of O$p$-planes and T-duality in stabilisation and scale separation.

Abstract

We complete the study initiated in \cite{Arboleya:2024vnp} and investigate three-dimensional (3D) flux vacua of type II orientifold reductions on twisted tori that include a single type of spacetime-filling O$p$-plane with $\,p=2,\ldots,9$. Restricting to $\textrm{SO}(3)$-invariant setups -- also known as RSTU-models -- and setting axions to zero, we exhaustively chart the landscape of 3D orientifold flux vacua. It consists of $\,56\,$ inequivalent multi-parametric families of AdS$_3$ and Mkw$_3$ flux vacua, all of them without negative masses in the spectrum of scalar fluctuations. Performing T-dualities, all the inequivalent vacua can be found in type IIB with either O9-, O5- or O3-planes. We show that: $i)\,$ type IIB with O$9$ fails to stabilise the volume of the internal space. $ii)\,$ type IIB with O5 realises the only cases of scale-separated AdS$_{3}$ vacua. $iii)\,$ type IIB with O$3$ provides only Mkw$_{3}$ vacua exhibiting a rich variety of supersymmetry-breaking patterns. Assuming that some mechanism (possibly non-perturbative) fixes the unstabilised modulus in type IIB with O$9$, we re-examine the possibility of achieving a weakly-coupled and scale-separated regime.

Figures (1)

• Figure 1: Diagram of inequivalent AdS$_{3}$ ($\bullet$) and Mkw$_{3}$ ($\blacktriangle$) flux vacua with vanishing axions in the RSTU-models. All of the vacua arise in type IIB orientifold reductions with O9-, O5- or O3-planes. Some of the vacua (those sitting at intersections) admit different realisations related by T-duality. $\blacktriangle$ (red triangle) is the trivial Mkw$_{3}$ vacuum with vanishing fluxes which, of course, exists in any duality frame. Despite the rich landscape, there are only two instances of weakly-coupled and scale-separated AdS$_3$ flux vacua which arise exclusively in a type IIB orientifold reduction with O$5$-planes.