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Affine Kac-Moody algebras, CHL strings and the classification of tops

Vincent Bouchard·Harald Skarke
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Abstract

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. 2003-12-24. Affine Kac-Moody algebras, CHL strings and the classification of tops. https://arxiv.org/abs/hep-th/0303218

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