{
  "id": "cond-mat/0205653",
  "version": "v1",
  "published": "2002-05-30T17:30:59.000Z",
  "updated": "2002-05-30T17:30:59.000Z",
  "title": "Non-commutative Chern-Simons for the Quantum Hall System and Duality",
  "authors": [
    "Eduardo Fradkin",
    "Vishnu Jejjala",
    "Robert G. Leigh"
  ],
  "comment": "21 pages (preprint), 3 figures",
  "journal": "Nucl.Phys. B642 (2002) 483-500",
  "categories": [
    "cond-mat.mes-hall",
    "hep-th"
  ],
  "abstract": "The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamic Chern-Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern-Simons theory has a perturbative momentum expansion. In this paper, we study this perturbation theory and show that the effective action, although commutative at leading order, is non-commutative. This conclusion is arrived at through a careful study of the three-point function of Chern-Simons gauge fields. The non-commutative gauge symmetry of this system is thus a quantum symmetry, which we show can only be fully realized only through the inclusion of all orders in perturbation theory. We discuss the duality between the two non-commutative descriptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-05-30T17:30:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum hall system",
      "non-commutative chern-simons",
      "non-commutative gauge symmetry",
      "perturbation theory",
      "chern-simons gauge fields"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/S0550-3213(02)00616-8"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 587746
    }
  }
}