## Friday, October 16, 2009

### F-theory papers go 3D

The prettiest hep-th preprint today is the last one and it was written by Clay Cordova at Harvard,
Decoupling Gravity in F-Theory (PDF)
The author, originally of Santa Fe, argues that in the context of F-theory phenomenology, there exist strong constraints on the singularities in the Calabi-Yau four-folds, coming from the condition that gravity decouples (a simplifying assumption, justified by the hugeness of the Planck mass i.e. gravity's approximate decoupling in reality). Geometrically, the condition means that the cycle S supporting the GUT group remains fixed in size while the total Calabi-Yau volume must be allowed to blow up.

A crash course on F-theory singularities and Fano threefolds is included. I guess that it may be useful for many readers to learn this material from Cordova. You know, if a high school student from 2003 knows such things, maybe we should follow, shouldn't we (despite the fact that all Fano threefolds are ultimately ruled out in the paper)? ;-)

But what is truly remarkable is the design of his paper. For example, this is the figure 1 with the general sketch of the branes within the F-theory compactification manifold and their intersections.

Click to zoom in a little bit. It's kind of logical that because F-theory is, in some sense, a 12-dimensional theory, the pictures should try to be multi-dimensional, too. ;-) After having read the paper, this guy clearly know what he's doing. He should only learn how to spell Planck correctly. :-)

However, I still feel that his requirement of the decoupling of gravity is too strict. Seven-branes carry the deficit angle of pi/12 and he wants to locally cancel it, by adding orientifold plans on top of the branes. Well, I would think that he should only try to decouple the propagating modes of gravity rather than the fixed contributions to the curvatures and deficit angles.