{
  "id": "1108.3035",
  "version": "v2",
  "published": "2011-08-15T17:18:40.000Z",
  "updated": "2011-11-02T18:25:06.000Z",
  "title": "Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition",
  "authors": [
    "Gernot Akemann",
    "Taro Nagao"
  ],
  "comment": "27 pages, 4 figures; v2 typos corrected, published version",
  "journal": "JHEP 10 (2011) 060",
  "doi": "10.1007/JHEP10(2011)060",
  "categories": [
    "math-ph",
    "hep-lat",
    "math.MP"
  ],
  "abstract": "We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in refs. [20,21]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with nu=0,1 we derive all spectral correlations functions in our model for finite-n, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chiral microscopic limit this yields all corresponding quenched eigenvalue correlation functions of the Hermitian Wilson operator.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-11-02T18:25:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hermitian wilson dirac operator",
      "random matrix theory",
      "chgue-gue transition",
      "quenched eigenvalue correlation functions",
      "gaussian unitary ensemble"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Journal of High Energy Physics",
      "year": 2011,
      "month": "Oct",
      "volume": 2011,
      "pages": 60
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 923973,
      "adsabs": "2011JHEP...10..060A"
    }
  }
}