What is F-theory?

String theory is an extension of quantum field theory which incorporates quantum gravity. In the process it reformulates many questions about field theory into questions about the geometry of extra dimensions. The 10-dimensional string backgrounds were found to reproduce the MSSM at low energies. However, this is only an intermediate step as we would like to answer many questions which are left unanswered by the MSSM. Many of these have to do the intrinsic difficulties of the theory of quantum gravity. But by effectively turning on gravity in 4-dimensions we can fulfil many of the phenomenological requirements which have a direct impact on particle physics. Interestingly enough, string theory allows us such freedom and in the process provides and intuitive geometric picture through the brane worlds approach. 

One of the key problems that one would like to address is the issue of gauge coupling unification. The most natural realization of such models is still some type of GUT. In particular, one would like to have realizations of such models in type II-B string theory where most of the recent progress in moduli stabilization, mediation of supersymmetry breaking and other issues have taken place. Attempts have been made at constructing D-brane GUT models which suffer from a number of difficulties like the lack of spinor representation for SO(10) or the perturbative vanishing of the top quark Yukawa couplings for SU(5) models. In fact, these difficulties arise because the past constructions relied heavily on local 7-branes. Such obstacles can be avoided by considering mutually non-local 7-branes. This enlarged class of models goes by the name of F-theory.  

F-theory encodes the physics of 7-branes in higher-dimensional geometry. Moreover, in certain limits F-theory is dual to the heterotic E8xE8 and the 11-dimensional M-theory. As a matter of fact, one of the most convenient ways to think about F-theory is via the duality with M-theory.