{
  "id": "0808.1720",
  "version": "v2",
  "published": "2008-08-12T19:42:15.000Z",
  "updated": "2008-12-20T10:53:56.000Z",
  "title": "Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory",
  "authors": [
    "Henriette Elvang",
    "Daniel Z. Freedman",
    "Michael Kiermaier"
  ],
  "comment": "42pp, 7 figures; v2: completion of 4-loop spin sum, typos corrected, new figure added",
  "journal": "JHEP 0904:009,2009",
  "doi": "10.1088/1126-6708/2009/04/009",
  "categories": [
    "hep-th"
  ],
  "abstract": "We prove that the MHV vertex expansion is valid for any NMHV tree amplitude of N=4 SYM. The proof uses induction to show that there always exists a complex deformation of three external momenta such that the amplitude falls off at least as fast as 1/z for large z. This validates the generating function for n-point NMHV tree amplitudes. We also develop generating functions for anti-MHV and anti-NMHV amplitudes. As an application, we use these generating functions to evaluate several examples of intermediate state sums on unitarity cuts of 1-, 2-, 3- and 4-loop amplitudes. In a separate analysis, we extend the recent results of arXiv:0808.0504 to prove that there exists a valid 2-line shift for any n-point tree amplitude of N=4 SYM. This implies that there is a BCFW recursion relation for any tree amplitude of the theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-20T10:53:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generating function",
      "sym theory",
      "unitarity sums",
      "n-point nmhv tree amplitudes",
      "n-point tree amplitude"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP",
      "journal": "Journal of High Energy Physics",
      "year": 2009,
      "month": "Apr",
      "volume": 2009,
      "number": 4,
      "pages": "009"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 792972,
      "adsabs": "2009JHEP...04..009E"
    }
  }
}