{
  "id": "hep-th/0303218",
  "version": "v2",
  "published": "2003-03-25T14:20:12.000Z",
  "updated": "2003-12-24T16:00:47.000Z",
  "title": "Affine Kac-Moody algebras, CHL strings and the classification of tops",
  "authors": [
    "Vincent Bouchard",
    "Harald Skarke"
  ],
  "comment": "28 pages, 10 figures",
  "journal": "Adv.Theor.Math.Phys. 7 (2003) 205-232",
  "categories": [
    "hep-th",
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-12-24T16:00:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine kac-moody algebras",
      "chl strings",
      "twisted kac-moody algebra",
      "classification",
      "elliptic fibration structure"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.4310/ATMP.2003.v7.n2.a1"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 615744,
      "adsabs": "2003hep.th....3218B"
    }
  }
}