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Advances in High Energy Physics
Volume 2011, Article ID 513436, 18 pages
Review Article

Toric Methods in F-Theory Model Building

1Institute for the Physics and Mathematics of the Universe (IPMU), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8583, Japan
2Institut für Theoretische Physik, TU Vienna, Wiedner Hauptstraβe 8-10, 1040 Vienna, Austria

Received 12 March 2011; Accepted 2 April 2011

Academic Editor: Yang-Hui He

Copyright © 2011 Johanna Knapp and Maximilian Kreuzer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.