{
  "id": "2008.00632",
  "version": "v1",
  "published": "2020-08-03T03:37:09.000Z",
  "updated": "2020-08-03T03:37:09.000Z",
  "title": "T-duality and the exotic chiral de Rham complex",
  "authors": [
    "Andrew Linshaw",
    "Varghese Mathai"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DG",
    "hep-th",
    "math.QA"
  ],
  "abstract": "Let $Z$ be a principal circle bundle over a base manifold $M$ equipped with an integral closed $3$-form $H$ called the flux. Let $\\widehat{Z}$ be the T-dual circle bundle over $M$ with flux $\\widehat{H}$. Han and Mathai recently constructed the $\\mathbb{Z}_2$-graded space of exotic differential forms $\\mathcal{A}^{\\bar{k}}(\\widehat{Z})$. It has an additional $\\mathbb{Z}$-grading such that the degree zero component coincides with the space of invariant twisted differential forms $\\Omega^{\\bar{k}}(\\widehat{Z}, \\widehat{H})^{\\widehat{\\mathbb{T}}}$, and it admits a differential that extends the twisted differential $d_{\\widehat{H}} = d + \\widehat{H}$. The T-duality isomorphism $\\Omega^{\\bar{k}}(Z,H)^{\\mathbb{T}} \\rightarrow \\Omega^{\\overline{k+1}}(\\widehat{Z}, \\widehat{H})^{\\widehat{\\mathbb{T}}}$ of Bouwknegt, Evslin and Mathai extends to an isomorphism $\\Omega^{\\bar{k}}(Z,H) \\rightarrow \\mathcal{A}^{\\overline{k+1}}(\\widehat{Z})$. In this paper, we introduce the exotic chiral de Rham complex $\\mathcal{A}^{\\text{ch},\\widehat{H},\\bar{k}}(\\widehat{Z})$ which contains $\\mathcal{A}^{\\bar{k}}(\\widehat{Z})$ as the weight zero subcomplex. We give an isomorphism $\\Omega^{\\text{ch},H,\\bar{k}}(Z) \\rightarrow \\mathcal{A}^{\\text{ch},\\widehat{H},\\overline{k+1}}(\\widehat{Z})$ where $\\Omega^{\\text{ch},H,\\bar{k}}(Z)$ denotes the twisted chiral de Rham complex of $Z$, which chiralizes the above T-duality map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-03T03:37:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rham complex",
      "exotic chiral",
      "degree zero component coincides",
      "exotic differential forms",
      "invariant twisted differential forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}