One of the points of F-theory is that it *may* be imagined to be a 12-dimensional theory – however one in which two dimensions are compactified on a tiny, infinitesimal two-torus.

But the supersymmetry generators are exactly those that are fully compactible with the 12-dimensional interpretation – after all, all "type IIB supercharges" in F-theory transform as a chiral spinor in 12 dimensions. So the logic of the proof that the background is Calabi-Yau is really the same.

The "Calabi-Yau 4-folds" of F-theory don't really have all the moduli because the two directions among the 12 are infinitesimal. But one may show that the complex structure may be defined just like for generic Calabi-Yaus.

Alternatively, you may just construct an analogous proof directly for F-theory. But the essence will be analogous. The holonomy group has to be restricted analogously.

This post imported from StackExchange Physics at 2014-03-17 06:10 (UCT), posted by SE-user Luboš Motl