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Advances in High Energy Physics
Volume 2011 (2011), Article ID 204576, 14 pages
Research Article

Chern-Simons: Fano and Calabi-Yau

1Theoretical Physics Group, Blackett Laboratory, Imperial College, London SW7 2AZ, UK
2KITP, University of California, Santa Barbara, CA 93106-4030, USA
3Rudolf Peierls Centre for Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, UK
4Collegium Mertonense in Academia Oxoniensi, Merton College, Oxford OX1 4JD, UK
5Mathematical Institute, Oxford University, 24-29 St. Giles', Oxford OX1 3LB, UK

Received 13 October 2010; Accepted 6 March 2011

Academic Editor: André Lukas

Copyright © 2011 Amihay Hanany and Yang-Hui He. 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 present the complete classification of smooth toric Fano threefolds, known to the algebraic geometry literature, and perform some preliminary analyses in the context of brane tilings and Chern-Simons theory on M2-branes probing Calabi-Yau fourfold singularities. We emphasise that these 18 spaces should be as intensely studied as their well-known counterparts: the del Pezzo surfaces.