Smearing orientifolds in flux compactifications can be OK

Abstract

We present explicit examples of supergravity solutions corresponding to backreacting localised (non-intersecting) O6 planes in flux reductions of massive IIA supergravity and address some criticism towards the very existence of such solutions. We verify in detail how the smeared orientifold solution becomes a good approximation to the localised solution in the large volume/weak coupling limit, as expected. We also find an exotic solution where prior to backreaction the internal space has a boundary and when backreaction is included the boundary disappears and the space closes off. The exotic example is however outside of the supergravity approximation everywhere.

Scale-separated AdS$_4$ vacua of IIA orientifolds and M-theory

“…In particular, [21] and [26] 3 computed the backreaction of O6 sources in the DGKT vacua at leading order in perturbation theory and found no obstacle to the existence of a solution. Analogous conclusions can be drawn in no-scale Minkowski compactifications [28] (see also [29]).…”

Three-dimensional flux vacua from IIB on co-calibrated G2 orientifolds

“…This is a non-trivial check for the validity of the effective theory derived from the smeared solution and implies that there should be an underlying full solution in IIB where the orientifold sources are localized. Indeed, there are instances where the smearing can be "OK" [35,40,41]. We leave the interesting exercise of finding the underlying un-smeared solutions for the future.…”

Comments on classical AdS flux vacua with scale separation

“…The only available 10D picture is one in which the O6 planes are smeared over the G2 space [13], just as for the DGKT vacua [12,22,23]. In the recent years this has been understood better, and for nonintersecting O6 planes in massive IIA the explicit backreaction was shown to be consistent with the smeared approximation [24] whereas for the intersecting case reassuring results were obtained at first-order in a backreaction series [25,26]. A generalisation of the DGKT solutions without Romans mass exists, and a preliminary lift to 11d has not revealed any signs of a troublesome backreaction either [3], despite the claims in [20].…”