New supersymmetric vacua on solvmanifolds

TL;DR

This work identifies new SUSY Minkowski flux vacua in type II on 4d Minkowski × 6d solvmanifolds with localized $O_p$-$D$ sources, demonstrating that the corresponding solvmanifolds can be Calabi–Yau with explicit metrics and are not T-dual to torus vacua. After warming up with nilmanifold examples, the authors construct truly new vacua on the $s_3$ algebra for $O_p$ with $p=4,5,6,7,8$, each admitting $SU(3)$ or orthogonal $SU(2)$ structures, and show they remain not torus-dual under Buscher duality. A key finding is that certain vacua display wrapped subspaces with non-closed smeared volume forms, enabling constant RR flux terms in the Bianchi identities and enabling full localization without torus duals. They further prove that the $s_3$ solvmanifolds are Calabi–Yau in the smeared fluxless limit, while the $s_1$ and $s_2$ cases are Ricci-flat Kähler but not Calabi–Yau due to torsion class constraints, highlighting distinct geometric roles for these algebras in flux compactifications.

Abstract

We obtain new supersymmetric flux vacua of type II supergravities on four-dimensional Minkowski times six-dimensional solvmanifolds. The orientifold O4, O5, O6, O7, or O8-planes and D-branes are localized. All vacua are in addition not T-dual to a vacuum on the torus. The corresponding solvmanifolds are proven to be Calabi-Yau, with explicit metrics. Other Ricci flat solvmanifolds are shown to be only Kähler.