F-Theory on Calabi-Yau manifolds

Question

Why F-theory picks Calabi-Yau manifolds as backgrounds? Is there a similar argument like the one in heterotic/IIA,B which singles out Calabi-Yau manifolds based on the requirement of space-time supersymmetry? If there is no 12-dimensional supergravity (hence no 12-dim SUSY variations) then how one can show that the solution of the killing-spinor equations chooses Calabi-Yau manifolds?

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

Answer 1

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