Taxonomy of type II orientifold flux vacua in 3D

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 $p=2,\dots ,9$. Restricting to $\text{SO}(3)$-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.

41 pages, 1 figure, 10 tables