{
  "id": "2402.01615",
  "version": "v2",
  "published": "2024-02-02T18:26:09.000Z",
  "updated": "2024-07-02T09:10:33.000Z",
  "title": "Computation of Quark Masses from String Theory",
  "authors": [
    "Andrei Constantin",
    "Cristofero S. Fraser-Taliente",
    "Thomas R. Harvey",
    "Andre Lukas",
    "Burt Ovrut"
  ],
  "comment": "Dedicated to the memory of Graham G. Ross",
  "categories": [
    "hep-th"
  ],
  "abstract": "We present a numerical computation, based on neural network techniques, of the physical Yukawa couplings in a heterotic string theory compactification on a smooth Calabi-Yau threefold with non-standard embedding. The model belongs to a large class of heterotic line bundle models that have previously been identified and whose low-energy spectrum precisely matches that of the MSSM plus fields uncharged under the Standard Model group. The relevant quantities for the calculation, that is, the Ricci-flat Calabi-Yau metric, the Hermitian Yang-Mills bundle metrics and the harmonic bundle-valued forms, are all computed by training suitable neural networks. For illustration, we consider a one-parameter family in complex structure moduli space. The computation at each point along this locus takes about half a day on a single twelve-core CPU. Our results for the Yukawa couplings are estimated to be within 10\\% of the expected analytic result. We find that the effect of the matter field normalisation can be significant and can contribute towards generating hierarchical couplings. We also demonstrate that a zeroth order, semi-analytic calculation, based on the Fubini-Study metric and its counterparts for the bundle metric and the bundle-valued forms, leads to roughly correct results, about 25\\% away from the numerical ones. The method can be applied to other heterotic line bundle models and generalised to other constructions, including to F-theory models.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-02T09:10:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heterotic line bundle models",
      "quark masses",
      "computation",
      "yukawa couplings",
      "complex structure moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}