{
  "id": "1111.1463",
  "version": "v2",
  "published": "2011-11-07T01:06:00.000Z",
  "updated": "2011-11-18T02:53:02.000Z",
  "title": "Determinant and Weyl anomaly of Dirac operator: a holographic derivation",
  "authors": [
    "Rodrigo Aros",
    "Danilo E Diaz"
  ],
  "comment": "11 pages; new comments and references added, typos corrected",
  "categories": [
    "math-ph",
    "gr-qc",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We present a holographic formula relating functional determinants: the fermion determinant in the one-loop effective action of bulk spinors in an asymptotically locally AdS background, and the determinant of the two-point function of the dual operator at the conformal boundary. The formula originates from AdS/CFT heuristics that map a quantum contribution in the bulk partition function to a subleading large-N contribution in the boundary partition function. We use this holographic picture to address questions in spectral theory and conformal geometry. As an instance, we compute the type-A Weyl anomaly and the determinant of the iterated Dirac operator on round spheres, express the latter in terms of Barnes' multiple gamma function and gain insight into a conjecture by B\\\"ar and Schopka.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-18T02:53:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirac operator",
      "weyl anomaly",
      "holographic derivation",
      "holographic formula relating functional determinants",
      "bulk partition function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/45/12/125401",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2012,
      "month": "Mar",
      "volume": 45,
      "number": 12,
      "pages": 125401
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 944782,
      "adsabs": "2012JPhA...45l5401A"
    }
  }
}