{
  "id": "1208.6153",
  "version": "v2",
  "published": "2012-08-30T12:37:12.000Z",
  "updated": "2012-09-25T09:37:25.000Z",
  "title": "Squaring the Magic",
  "authors": [
    "Sergio L. Cacciatori",
    "Bianca L. Cerchiai",
    "Alessio Marrani"
  ],
  "comment": "21 pages, 1 figure, 20 tables; reference added",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We construct and classify all possible Magic Squares (MS's) related to Euclidean or Lorentzian rank-3 simple Jordan algebras, both on normed division algebras and split composition algebras. Besides the known Freudenthal-Rozenfeld-Tits MS, the single-split G\\\"unaydin-Sierra-Townsend MS, and the double-split Barton-Sudbery MS, we obtain other 7 Euclidean and 10 Lorentzian novel MS's. We elucidate the role and the meaning of the various non-compact real forms of Lie algebras, entering the MS's as symmetries of theories of Einstein-Maxwell gravity coupled to non-linear sigma models of scalar fields, possibly endowed with local supersymmetry, in D = 3, 4 and 5 space-time dimensions. In particular, such symmetries can be recognized as the U-dualities or the stabilizers of scalar manifolds within space-time with standard Lorentzian signature or with other, more exotic signatures, also relevant to suitable compactifications of the so-called M*- and M'- theories. Symmetries pertaining to some attractor U-orbits of magic supergravities in Lorentzian space-time also arise in this framework.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-25T09:37:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "space-time",
      "split composition algebras",
      "simple jordan algebras",
      "symmetries",
      "double-split barton-sudbery ms"
    ],
    "publication": {
      "doi": "10.4310/ATMP.2015.v19.n5.a1"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1183847,
      "adsabs": "2012arXiv1208.6153C"
    }
  }
}