Chiral Matter in F-Theory Compactifications

Abstract

String theory provides a framework to construct quantum theories of gravity that are UV-complete. It is a key interest of string phenomenology to realize verifiable models of particle physics such as extensions of the Standard Model in this framework. F-theory provides a technique to translate the gauge theory of Type IIB superstring theory on orientifolds into geometric quantities, strictly speaking, into singularities of an elliptically fibered Calabi-Yau fourfold. We review a new method to compute the number of chiral particles, called the chiral index, in terms of a background flux and the base manifold in a general way. This method utilizes the intersection theory of resolved elliptic fourfolds, which is deeply connected to the gauge theory and the chiral index. This intersection theory also appears in the log-monodromy matrices associated with the singularities at large complex-structure in the moduli space of the mirror manifold of the resolved elliptic fourfold. Our goal is to examine how much information about the chiral index can be extracted from this large complex-structure regime.