Abstract
AbstractWe construct AdS4 flux vacua of type IIA string theory in the supergravity (large volume, small ) regime, including the backreaction of O6‐planes. Our solutions are the localized versions of the smeared solutions on Calabi‐Yau orientifolds studied by DeWolfe, Giryavets, Kachru and Taylor and in other works. We find that the O‐plane backreaction in these solutions generates warping, a varying dilaton, non‐closed RR field strengths and internal curvature. Just like their smeared counterparts, the localized solutions admit stabilized moduli, a parametric control over string corrections and a parametric separation between the AdS and KK scales. Our explicit expressions furthermore make precise the common lore that smeared solutions should approximate the exact ones in the large‐volume, small‐ limit. Finally, our solutions appear to violate a recent swampland conjecture about an absence of scale separation in supersymmetric AdS vacua. We make a simple observation explaining why this happens in these solutions in contrast to most other AdS solutions in string theory.
Highlights
A recurring criticism in the literature is that the DGKT solutions are not trustworthy because they were obtained in an approximation where the O6-planes are smeared, i.e., their tension and charge densities are assumed to be uniformly distributed over the compact space for simplicity
We computed the O6-plane backreaction in type IIA AdS flux vacua on Calabi-Yau orientifolds, which were previously studied in the smeared approximation in several other works [1,2,3,4,5,6]
We performed our analysis in the usual regime of large volumes and small gs, where string theory is well-approximated by 10d supergravity
Summary
The internal metric gmn is Ricci-flat in the smeared solutions but curved if the O6-plane backreaction is included, as we shall see below. Since we are only interested in vacuum solutions, we will assume that the supergravity fields do not depend on the AdS coordinates xμ. We only allow NSNS and RR forms with legs along internal directions. The contribution of the localized O6-planes to the equations of motion is taken into account by terms involving delta distributions.. We denote by δ(πi) the delta distribution with support on the 3-cycle πi 3-form that integrates to one wrapped over the by the ith dual cycle. The RR and NSNS field equations (in string frame) are. In the explicit example discussed, some of the O-planes are diagonal with respect to the ym coordinates, leading to different expressions for Πi,mn
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