{
  "id": "1405.2074",
  "version": "v4",
  "published": "2014-05-08T20:00:04.000Z",
  "updated": "2014-12-13T18:03:29.000Z",
  "title": "Geometric constraints in dual F-theory and heterotic string compactifications",
  "authors": [
    "Lara B. Anderson",
    "Washington Taylor"
  ],
  "comment": "81 pages, 2 figures; v2, v3: references added, minor corrections; v4: minor errors, Table 5 corrected",
  "categories": [
    "hep-th",
    "math.AG"
  ],
  "abstract": "We systematically analyze a broad class of dual heterotic and F-theory models that give four-dimensional supergravity theories, and compare the geometric constraints on the two sides of the duality. Specifically, we give a complete classification of models where the heterotic theory is compactified on a smooth Calabi-Yau threefold that is elliptically fibered with a single section and carries smooth irreducible vector bundles, and the dual F-theory model has a corresponding threefold base that has the form of a P^1 bundle. We formulate simple conditions for the geometry on the F-theory side to support an elliptically fibered Calabi-Yau fourfold. We match these conditions with conditions for the existence of stable vector bundles on the heterotic side, and show that F-theory gives new insight into the conditions under which such bundles can be constructed. In particular, we find that many allowed F-theory models correspond to vector bundles on the heterotic side with exceptional structure groups, and determine a topological condition that is only satisfied for bundles of this type. We show that in many cases the F-theory geometry imposes a constraint on the extent to which the gauge group can be enhanced, corresponding to limits on the way in which the heterotic bundle can decompose. We explicitly construct all (4962) F-theory threefold bases for dual F-theory/heterotic constructions in the subset of models where the common twofold base surface is toric, and give both toric and non-toric examples of the general results.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-03T00:42:35.000Z",
      "comment": "81 pages, 2 figures; v2, v3: references added, minor corrections",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-12-13T18:03:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heterotic string compactifications",
      "dual f-theory",
      "geometric constraints",
      "f-theory model",
      "carries smooth irreducible vector bundles"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/JHEP08(2014)025",
      "journal": "Journal of High Energy Physics",
      "year": 2014,
      "month": "Aug",
      "volume": 2014,
      "pages": 25
    },
    "note": {
      "typesetting": "TeX",
      "pages": 81,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1295508,
      "adsabs": "2014JHEP...08..025A"
    }
  }
}