Lectures on F-theory compactifications and model building

TL;DR

This paper provides a comprehensive overview of F-theory compactifications, covering foundational concepts, geometric frameworks, and phenomenological applications, especially in GUT model building and flux mechanisms.

Contribution

It introduces a pedagogical approach to F-theory, detailing the use of Tate models and spectral cover construction for constructing and analyzing F-theory GUT models.

Findings

Explains the connection between F-theory and Type IIB orientifolds.

Describes the geometry of elliptic fibrations and gauge group emergence.

Reviews GUT breaking via hypercharge flux in F-theory models.

Abstract

These lecture notes are devoted to formal and phenomenological aspects of F-theory. We begin with a pedagogical introduction to the general concepts of F-theory, covering classic topics such as the connection to Type IIB orientifolds, the geometry of elliptic fibrations and the emergence of gauge groups, matter and Yukawa couplings. As a suitable framework for the construction of compact F-theory vacua we describe a special class of Weierstrass models called Tate models, whose local properties are captured by the spectral cover construction. Armed with this technology we proceed with a survey of F-theory GUT models, aiming at an overview of basic conceptual and phenomenological aspects, in particular in connection with GUT breaking via hypercharge flux.