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The Toric Approach To F-Theory Model Building, Herbie L. Smith

Honors Theses and Capstones

We describe the theoretical motivation for F-theory as a non-perturbative generalization of string theory. The four complex-dimensional compactification spaces of F-theory, called elliptically-fibered Calabi-Yau manifolds, consist of the six compact dimensions of string theory, plus a two-dimensional fiber that describes the string coupling field as a function of position on the string theory manifold. The methods of toric geometry are developed and applied to construct examples of elliptically-fibered Calabi-Yau manifolds. We analyze in detail models in which the fiber is free of singularities as a test bed for a more general analysis.