TASI Lectures on F-theory

TL;DR

F-theory provides a comprehensive geometric framework for studying non-perturbative string compactifications, linking gauge theories and elliptic fibrations, with broad applications in string model building and quantum gravity.

Contribution

This paper offers an extensive introduction to F-theory, emphasizing the geometric dictionary connecting elliptic fibrations with physical concepts like 7-branes and gauge backgrounds.

Findings

Elucidation of the F-theory dictionary relating geometry and physics.

Analysis of elliptic fibration behavior in various codimensions.

Insights into the Mordell-Weil group and gauge backgrounds in F-theory.

Abstract

F-theory is perhaps the most general currently available approach to study non-perturbative string compactifications in their geometric, large radius regime. It opens up a wide and ever-growing range of applications and connections to string model building, quantum gravity, (non-perturbative) quantum field theories in various dimensions and mathematics. Its computational power derives from the geometrisation of physical reasoning, establishing a deep correspondence between fundamental concepts in gauge theory and beautiful structures of elliptic fibrations. These lecture notes, which are an extended version of my lectures given at TASI 2017, introduce some of the main concepts underlying the recent technical advances in F-theory compactifications and their various applications. The main focus is put on explaining the F-theory dictionary between the local and global data of an elliptic fibration and the physics of 7-branes in Type IIB compactifications to various dimensions via duality with M-theory. The geometric concepts underlying this dictionary include the behaviour of elliptic fibrations in codimension one, two, three and four, the Mordell-Weil group of rational sections, and the Deligne cohomology group specifying gauge backgrounds.