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

Bouchard, Vincent; Skarke, Harald

Adv. Theor. Math. Phys., Tome 7 (2003) no. 5, p. 205-232 / Harvested from Project Euclid

Résumé

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.

Publié le : 2003-04-14
Classification:

@article{1112627632,
     author = {Bouchard, Vincent and Skarke, Harald},
     title = {Affine Kac-Moody algebras, CHL strings and the classification of tops},
     journal = {Adv. Theor. Math. Phys.},
     volume = {7},
     number = {5},
     year = {2003},
     pages = { 205-232},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1112627632}
}

Bouchard, Vincent; Skarke, Harald. Affine Kac-Moody algebras, CHL strings and the classification of tops. Adv. Theor. Math. Phys., Tome 7 (2003) no. 5, pp.  205-232. http://gdmltest.u-ga.fr/item/1112627632/