Decoupling gravity in F-theory. (English) Zbl 1258.81083

Summary: We study 7-brane \(\text{SU}(5)\) 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.


81V22 Unified quantum theories
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V17 Gravitational interaction in quantum theory
83E30 String and superstring theories in gravitational theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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