{
  "id": "1412.0166",
  "version": "v1",
  "published": "2014-11-29T23:34:02.000Z",
  "updated": "2014-11-29T23:34:02.000Z",
  "title": "Twisted chiral de Rham complex, generalized geometry, and T-duality",
  "authors": [
    "Andrew Linshaw",
    "Varghese Mathai"
  ],
  "categories": [
    "math.DG",
    "hep-th",
    "math.QA"
  ],
  "abstract": "The chiral de Rham complex of Malikov, Schechtman, and Vaintrob, is a sheaf of differential graded vertex algebras that exists on any smooth manifold $Z$, and contains the ordinary de Rham complex at weight zero. Given a closed 3-form $H$ on $Z$, we construct the twisted chiral de Rham differential $D_H$, which coincides with the ordinary twisted differential in weight zero. We show that its cohomology vanishes in positive weight and coincides with the ordinary twisted cohomology in weight zero. As a consequence, we propose that in a background flux, Ramond-Ramond fields can be interpreted as $D_H$-closed elements of the chiral de Rham complex. Given a T-dual pair of principal circle bundles $Z, \\widehat{Z}$ with fluxes $H, \\widehat{H}$, we establish a degree-shifting linear isomorphism between the $S^1$-invariant chiral de Rham complexes of $Z$ and $\\widehat{Z}$. At weight zero, it restricts to the usual isomorphism of $S^1$-invariant differential forms, and induces the usual isomorphism in twisted cohomology. This is interpreted as T-duality in type II string theory from a loop space perspective. A key ingredient in defining this isomorphism is the language of Courant algebroids, which clarifies the notion of functoriality of the chiral de Rham complex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-29T23:34:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rham complex",
      "twisted chiral",
      "weight zero",
      "generalized geometry",
      "usual isomorphism"
    ],
    "publication": {
      "doi": "10.1007/s00220-015-2403-z",
      "journal": "Communications in Mathematical Physics",
      "year": 2015,
      "month": "Oct",
      "volume": 339,
      "number": 2,
      "pages": 663
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1331829,
      "adsabs": "2015CMaPh.339..663L"
    }
  }
}