Toric Methods in F-theory Model Building

TL;DR

This paper reviews the use of toric geometry in constructing and analyzing global F-theory GUT models, providing tools and methods for systematic model building using computational software.

Contribution

It introduces a comprehensive framework combining toric geometry and F-theory GUTs, including practical computational techniques with PALP software.

Findings

Systematic construction of Calabi-Yau fourfolds supporting F-theory GUTs

Application of toric geometry tools to F-theory model analysis

Demonstration of large class of models via computational methods

Abstract

In this review article we discuss recent constructions of global F-theory GUT models and explain how to make use of toric geometry to do calculations within this framework. After introducing the basic properties of global F-theory GUTs we give a self-contained review of toric geometry and introduce all the tools that are necessary to construct and analyze global F-theory models. We will explain how to systematically obtain a large class of compact Calabi-Yau fourfolds which can support F-theory GUTs by using the software package PALP.