Taxonomy of type II orientifold flux vacua in 3D

TL;DR

This paper classifies and analyzes three-dimensional flux vacua in type II orientifold string theories, identifying various stable AdS and Minkowski solutions, and exploring their properties under T-duality and moduli stabilization.

Contribution

It provides a comprehensive taxonomy of 3D orientifold flux vacua, including new families of solutions and their dualities, with detailed stability and scale separation analysis.

Findings

56 inequivalent flux vacua families identified

Type IIB with O5-planes yields scale-separated AdS3 vacua

Type IIB with O3-planes produces diverse Minkowski vacua

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.