{
  "id": "1512.06182",
  "version": "v1",
  "published": "2015-12-19T03:10:08.000Z",
  "updated": "2015-12-19T03:10:08.000Z",
  "title": "Entanglement entropy of a Maxwell field on the sphere",
  "authors": [
    "Horacio Casini",
    "Marina Huerta"
  ],
  "comment": "18 pages, 5 figures",
  "categories": [
    "hep-th"
  ],
  "abstract": "We compute the logarithmic coefficient of the entanglement entropy on a sphere for a Maxwell field in $d=4$ dimensions. In spherical coordinates the problem decomposes into one dimensional ones along the radial coordinate for each angular momentum. We show the entanglement entropy of a Maxwell field is equivalent to the one of two identical massless scalars from which the mode of $l=0$ has been removed. This shows the relation $c^M_{\\log}=2 (c^S_{\\log}-c^{S_{l=0}}_{\\log})$ between the logarithmic coefficient in the entropy for a Maxwell field $c^M_{\\log}$, the one for a $d=4$ massless scalar $c_{\\log}^S$, and the logarithmic coefficient $c^{S_{l=0}}_{\\log}$ for a $d=2$ scalar with Dirichlet boundary condition at the origin. Using the accepted values for these coefficients $c_{\\log}^S=-1/90$ and $c^{S_{l=0}}_{\\log}=1/6$ we get $c^M_{\\log}=-16/45$, which coincides with Dowker's calculation, but does not match the coefficient $-\\frac{31}{45}$ in the trace anomaly for a Maxwell field. We have numerically evaluated these three numbers $c^M_{\\log}$, $c^S_{\\log}$ and $c^{S_{l=0}}_{\\log}$, verifying the relation, as well as checked they coincide with the corresponding logarithmic term in mutual information of two concentric spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-19T03:10:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maxwell field",
      "entanglement entropy",
      "logarithmic coefficient",
      "dirichlet boundary condition",
      "massless scalar"
    ],
    "publication": {
      "doi": "10.1103/PhysRevD.93.105031"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151206182C",
      "inspire": 1410908
    }
  }
}