Decoupling gravity in F-theory

Abstract

We study seven-brane SU(5) GUT models of string phenomenology which can be consistently analyzed in a purely local framework. The requirement that gravity can decouple constrains the form of four-dimensional physics as well as the geometry of spacetime. We rule out a large family of candidate UV completions of such models and derive a priori constraints on the local singularities of compact elliptic Calabi– Yau four-folds. These constraints are strong enough to obstruct a wide class of brane constructions from UV completion in string theory. It is demonstrated that consistent local models always have exotic Yukawa coupling structures, and hidden sectors or interesting non-perturbative superpotentials which merit further investigation.