{
  "id": "2108.10297",
  "version": "v1",
  "published": "2021-08-23T17:14:43.000Z",
  "updated": "2021-08-23T17:14:43.000Z",
  "title": "Extended Field Theories as higher Kaluza-Klein theories",
  "authors": [
    "Luigi Alfonsi"
  ],
  "comment": "PhD Thesis, 309 pages, 8 tables, 21 figures",
  "categories": [
    "hep-th",
    "math-ph",
    "math.DG",
    "math.MP",
    "math.QA"
  ],
  "abstract": "Extended Field Theories include Double Field Theory (DFT) and Exceptional Field Theory, which are respectively the T- and U-duality covariant formulations of the supergravity limit of String Theory and M-theory. Extended Field Theories do not live on spacetime, but on an extended spacetime, locally modelled on the space underlying the fundamental representation of the duality group. Despite its importance in M-theory, however, the global understanding of Extended Field Theories is still an open problem. In this thesis we propose a global geometric formulation of Extended Field Theory. Recall that ordinary Kaluza-Klein theory unifies a metric with a gauge field on a principal bundle. We propose a generalisation of the Kaluza-Klein principle which unifies a metric and a higher gauge field on a principal infinity-bundle. This is achieved by introducing an atlas for the principal infinity-bundle, whose local charts can be naturally identified with the ones of Extended Field Theory. Thus, DFT is interpreted as a higher Kaluza-Klein theory set on the total space of a bundle gerbe underlying Kalb-Ramond field. As first application, we define the higher Kaluza-Klein monopole by naturally generalising the ordinary Gross-Perry monopole. Then we show that this monopole is exactly the NS5-brane of String Theory. Secondly, we show that our higher geometric formulation gives automatically rise to global abelian T-duality and global Poisson-Lie T-duality. In particular, we globally recover the abelian T-fold and we define the notion of Poisson-Lie T-fold. Crucially, we will investigate the global geometric formulation of tensor hierarchies and gauged supergravity. In particular, we will provide a global formulation of generalised Scherk-Schwarz reductions and we will discuss their global non-geometric properties. Finally, we explore the T-duality covariant geometric quantisation of DFT.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-23T17:14:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C08",
      "53D18",
      "83E30"
    ],
    "keywords": [
      "extended field theory",
      "global geometric formulation",
      "higher kaluza-klein theory set",
      "t-duality covariant geometric quantisation",
      "principal infinity-bundle"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 309,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}