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April 2003 Affine Kac-Moody algebras, CHL strings and the classification of tops
Vincent Bouchard, Harald Skarke
Adv. Theor. Math. Phys. 7(2): 205-232 (April 2003).


Candelas and Font introduced the notion of a 'top' as half of a three dimensional reflexive polytope and noticed that Dynkin diagrams of enhanced gauge groups in string theory can be read off from them. We classify all tops satisfying a generalized definition as a lattice polytope with one facet containing the origin and the other facets at distance one from the origin. These objects torically encode the local geometry of a degeneration of an elliptic fibration. We give a prescription for assigning an affine, possibly twisted Kac-Moody algebra to any such top (and more generally to any elliptic fibration structure) in a precise way that involves the lengths of simple roots and the coefficients of null roots. Tops related to twisted Kac-Moody algebras can be used to construct string compactifications with reduced rank of the gauge group.


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Vincent Bouchard. Harald Skarke. "Affine Kac-Moody algebras, CHL strings and the classification of tops." Adv. Theor. Math. Phys. 7 (2) 205 - 232, April 2003.


Published: April 2003
First available in Project Euclid: 4 April 2005

MathSciNet: MR2015164

Rights: Copyright © 2003 International Press of Boston

Vol.7 • No. 2 • April 2003
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