GUTs and Exceptional Branes in F-theory - I

TL;DR

This paper develops tools for constructing GUT models in F-theory, linking geometry to physical features like gauge groups and matter content, and explores the role of topological theories and defects in this framework.

Contribution

It introduces a geometric approach to GUT model building in F-theory using topologically twisted theories and surface defects to encode physical properties.

Findings

Geometry determines gauge groups, matter, and Yukawa couplings.

Surface defects in topological theory correspond to matter propagation.

Singularity unfolding matches defect properties in the topological theory.

Abstract

Motivated by potential phenomenological applications, we develop the necessary tools for building GUT models in F-theory. This approach is quite flexible because the local geometrical properties of singularities in F-theory compactifications encode the physical content of the theory. In particular, we show how geometry determines the gauge group, matter content and Yukawa couplings of a given model. It turns out that these features are beautifully captured by a four-dimensional topologically twisted N=4 theory which has been coupled to a surface defect theory on which chiral matter can propagate. From the vantagepoint of the four-dimensional topological theory, these defects are surface operators. Specific intersection points of these defects lead to Yukawa couplings. We also find that the unfolding of the singularity in the F-theory geometry precisely matches to properties of the topological theory with a defect.