Massive IIA flux compactifications and U-dualities

TL;DR

This paper investigates the complex structure of massive IIA flux compactifications, exploring their dualities, geometric back reactions, and potential M-theory and F-theory interpretations, highlighting challenges in their rigorous formulation.

Contribution

It provides a new perspective on the geometric and duality properties of massive IIA flux compactifications, proposing a framework akin to F-theory for understanding their generic limits.

Findings

Approximate double T-duality relates backgrounds to twisted tori.

Back reaction of orientifolds is significant, complicating geometry.

Entropy calculations suggest M2-brane scaling in certain limits.

Abstract

We attempt to find a rigorous formulation for the massive type IIA orientifold compactifications of string theory introduced in hep-th/0505160. An approximate double T-duality converts this background into IIA string theory on a twisted torus, but various arguments indicate that the back reaction of the orientifold on this geometry is large. In particular, an AdS calculation of the entropy suggests a scaling appropriate for N M2-branes, in a certain limit of the compactification, though not the one studied in hep-th/0505160. The M-theory lift of this specific regime is not 4 dimensional. We suggest that the generic limit of the background corresponds to a situation analogous to F-theory, where the string coupling is small in some regions of a compact geometry, and large in others, so that neither a long wavelength 11D SUGRA expansion, nor a world sheet expansion exists for these compactifications. We end with a speculation on the nature of the generic compactification.