{
  "id": "cond-mat/0503728",
  "version": "v3",
  "published": "2005-03-31T00:26:54.000Z",
  "updated": "2005-06-22T09:37:39.000Z",
  "title": "Asymptotic Freedom of Elastic Strings and Barriers",
  "authors": [
    "Peter Orland",
    "Jing Xiao"
  ],
  "comment": "Text slightly improved, bibilography corrected, more typos corrected, still Latex 7 pages",
  "journal": "Phys.Rev. B72 (2005) 052503",
  "doi": "10.1103/PhysRevB.72.052503",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.supr-con",
    "hep-lat",
    "hep-th"
  ],
  "abstract": "We study the problem of a quantized elastic string in the presence of an impenetrable wall. This is a two-dimensional field theory of an N-component real scalar field $\\phi$ which becomes interacting through the restriction that the magnitude of $\\phi$ is less than $\\phi_{\\rm max}$, for a spherical wall of radius $\\phi_{\\rm max}$. The N=1 case is a string vibrating in a plane between two straight walls. We review a simple nonperturbative argument that there is a gap in the spectrum, with asymptotically-free behavior in the coupling (which is the reciprocal of $\\phi_{\\rm max}$) for N greater than or equal to one. This scaling behavior of the mass gap has been disputed in some of the recent literature. We find, however, that perturbation theory and the 1/N expansion each confirms that these theories are asymptotically free. The large N limit coincides with that of the O(N) nonlinear sigma model. A theta parameter exists for the N=2 model, which describes a string confined to the interior of a cylinder of radius $\\phi_{\\rm max}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-06-22T09:37:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elastic string",
      "asymptotic freedom",
      "n-component real scalar field",
      "two-dimensional field theory",
      "nonlinear sigma model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 679497
    }
  }
}