{
  "id": "math-ph/0008027",
  "version": "v2",
  "published": "2000-08-21T15:16:43.000Z",
  "updated": "2000-11-07T02:29:35.000Z",
  "title": "Conformal Field Theory and Doplicher-Roberts Reconstruction",
  "authors": [
    "Michael Mueger"
  ],
  "comment": "latex, 23 pages, documentclass fic-l, uses diagrams.tex. Final version. Relevance of Turaev's notion of braided crossed G-categories pointed out, otherwise minor changes",
  "journal": "Fields Inst. Commun. 30, 297-319 (2001)",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "After a brief review of recent rigorous results concerning the representation theory of rational chiral conformal field theories (RCQFTs) we focus on pairs (A,F) of conformal field theories, where F has a finite group G of global symmetries and A is the fixpoint theory. The comparison of the representation categories of A and F is strongly intertwined with various issues related to braided tensor categories. We explain that, given the representation category of A, the representation category of F can be computed (up to equivalence) by a purely categorical construction. The latter is of considerable independent interest since it amounts to a Galois theory for braided tensor categories. We emphasize the characterization of modular categories as braided tensor categories with trivial center and we state a double commutant theorem for subcategories of modular categories. The latter implies that a modular category M which has a replete full modular subcategory M_1 is equivalent to M_1 x M_2 where M_2=M\\cap M_1' is another modular subcategory. On the other hand, the representation category of A is not determined completely by that of F and we identify the needed additional data in terms of soliton representations. We comment on `holomorphic orbifold' theories, i.e. the case where F has trivial representation theory, and close with some open problems. We point out that our approach permits the proof of many conjectures and heuristic results on `simple current extensions' and `holomorphic orbifold models' in the physics literature on conformal field theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-11-07T02:29:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81T40",
      "81T05",
      "46L60",
      "18D10"
    ],
    "keywords": [
      "conformal field theory",
      "doplicher-roberts reconstruction",
      "representation category",
      "braided tensor categories",
      "modular category"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 532297,
      "adsabs": "2000math.ph...8027M"
    }
  }
}