{
  "id": "1806.05992",
  "version": "v1",
  "published": "2018-06-15T14:17:44.000Z",
  "updated": "2018-06-15T14:17:44.000Z",
  "title": "A Unique Connection for Born Geometry",
  "authors": [
    "Laurent Freidel",
    "Felix J. Rudolph",
    "David Svoboda"
  ],
  "comment": "47 pages",
  "categories": [
    "hep-th",
    "gr-qc"
  ],
  "abstract": "It has been known for a while that the effective geometrical description of compactified strings on $d$-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an $O(d,d)$ pairing $\\eta$ and an $O(2d)$ generalized metric $\\mathcal{H}$. More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing $\\omega$. The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure $(\\eta,\\omega,\\mathcal{H})$ and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-15T14:17:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "born geometry",
      "unique connection",
      "dimensional target spaces implies",
      "double field theory formulation",
      "tangent space directions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}