{
  "id": "1711.05669",
  "version": "v1",
  "published": "2017-11-15T17:05:07.000Z",
  "updated": "2017-11-15T17:05:07.000Z",
  "title": "Analytic continuation of dimensions in supersymmetric localization",
  "authors": [
    "Anastasios Gorantis",
    "Joseph A. Minahan",
    "Usman Naseer"
  ],
  "comment": "52 pages, 4 appendices, no figures",
  "categories": [
    "hep-th"
  ],
  "abstract": "We compute the perturbative partition functions for gauge theories with eight supersymmetries on spheres of dimension $d\\le5$, proving a conjecture by the second author. We apply similar methods to gauge theories with four supersymmetries on spheres with $d\\le3$. The results are valid for non-integer $d$ as well. We further propose an analytic continuation from $d=3$ to $d=4$ that gives the perturbative partition function for an $\\mathcal{N}=1$ gauge theory. The results are consistent with the free multiplets and the one-loop $\\beta$-functions for general $\\mathcal{N}=1$ gauge theories. We also consider the analytic continuation of an $\\mathcal{N}=1$-preserving mass deformation of the maximally supersymmetric gauge theory and compare to recent holographic results for $\\mathcal{N}=1^*$ super Yang-Mills. We find that the general structure for the real part of the free energy coming from the analytic continuation is consistent with the holographic results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-15T17:05:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "analytic continuation",
      "supersymmetric localization",
      "perturbative partition function",
      "holographic results",
      "maximally supersymmetric gauge theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}