Lectures on F-theory compactifications and model building

TL;DR

This work surveys F-theory as a nonperturbative framework for string phenomenology, highlighting how elliptic fibrations encode varying axio-dilaton profiles and 7-brane backreaction. It develops the toolkit to construct four-dimensional vacua via Weierstrass/Tate models, fluxes described by $G_4$, and matter/localization on curves and Yukawa points, with dual perspectives from M-theory and heterotic strings. The notes emphasize SU(5) GUT model building, including decoupling limits, GUT-breaking via hypercharge flux, and the interplay between global consistency and local model-building data. They also discuss the spectral cover approach and its role in engineering gauge flux and chiral matter, as well as current challenges in reconciling gauge coupling unification and proton stability in global compactifications.

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.