Classification of base geometries in F-theory

Abstract

F-theory is a powerful geometric framework to describe strongly coupled type JIB supcrstring theory. After we compactify F-theory on elliptically fibered Calabi-Yau manifolds of various dimensions, we produce a large number of minimal supergravity models in six or four spacetime dimensions. In this thesis, I will describe a current classification program of these elliptic Calabi-Yau manifolds. Specifically, I will be focusing on the part of classifying complex base manifolds of these elliptic fibrations. Besides the usual algebraic geometric description of these base manifolds, F-theory provides a physical language to characterize them as well. One of the most important physical feature of the bases is called the "non-Higgsable gauge groups", which is the minimal gauge group in the low energy supergravity model for any elliptic fibration on a specific base. I will present the general classification program of complex base surfaces and threefolds using algebraic geometry machinery and the language of non- Higgsable gauge groups. While the complex base surfaces can be completely classified in principle, the zoo of generic complex threefolds is not well understood. However, I will present an exploration of the subset of toric threefold bases. I will also describe examples of base manifolds with non-Higgsable U(1)s, which lead to supergravity models in four and six dimensions with a U(1) gauge group but no massless charged matter.