New supersymmetric AdS4 type II vacua

TL;DR

This work provides a concrete set of sufficient conditions for supersymmetric $AdS_4$ vacua in type II supergravity by requiring the internal manifold $\mathcal{M}_6$ to be locally a codimension-one foliation with five-dimensional leaves admitting a Sasaki-Einstein structure. It develops explicit IIA and IIB constructions from any Sasaki-Einstein 5-manifold, yielding pure-flux backgrounds with nonzero fluxes (including the Romans mass in IIA) and non-constant dilaton and warp factor, without sources. The IIA analysis distinguishes undeformed (massless) solutions with strict $SU(3)$ structure—where $\mathcal{M}_6$ is a Sasaki-Einstein fibration over a KE base and $F_2$ is exact— from mass-deformed solutions with dynamic $SU(3)\times SU(3)$ structure, governed by two coupled first-order ODEs for two unknown functions; the IIB side provides static $SU(2)$-structured vacua with explicit flux profiles and two Bianchi-identity branches. Collectively, these results extend the AdS$_4$/CFT$_3$ landscape by connecting Sasaki-Einstein geometry to flux compactifications, with uplifts to 11D Freund–Rubin spaces and links to well-known SE geometries such as $S^5$, $T^{1,1}$, and $Y^{p,q}$.

Abstract

Building on our recent results on dynamic SU(3)xSU(3) structures we present a set of sufficient conditions for supersymmetric AdS4xM6 backgrounds of type IIA/IIB supergravity. These conditions ensure that the background solves, besides the supersymmetry equations, all the equations of motion of type II supergravity. The conditions state that the internal manifold is locally a codimension-one foliation such that the five dimensional leaves admit a Sasaki-Einstein structure. In type IIA the supersymmetry is N=2, and the total six-dimensional internal space is locally an S^2 bundle over a four-dimensional Kaehler-Einstein base; in IIB the internal space is the direct product of a circle and a five-dimensional squashed Sasaki-Einstein manifold. Given any five-dimensional Sasaki-Einstein manifold we construct the corresponding families of type IIA/IIB vacua. The precise profiles of all the fields are determined at the solution and depend on whether one is in IIA or in IIB. In particular the background does not contain any sources, all fluxes (including the Romans mass in IIA) are generally non-zero, and the dilaton and warp factor are non-constant.