{
  "id": "1310.6360",
  "version": "v2",
  "published": "2013-10-23T20:00:03.000Z",
  "updated": "2014-12-23T00:25:48.000Z",
  "title": "Stability and Spectrum of Compactifications on Product Manifolds",
  "authors": [
    "Adam R. Brown",
    "Alex Dahlen"
  ],
  "comment": "52 pages, 4 figures; v2: footnote and references added",
  "journal": "Phys. Rev. D 90, 044047 (2014)",
  "doi": "10.1103/PhysRevD.90.044047",
  "categories": [
    "hep-th"
  ],
  "abstract": "We study the spectrum and perturbative stability of Freund-Rubin compactifications on $M_p \\times M_{Nq}$, where $M_{Nq}$ is itself a product of $N$ $q$-dimensional Einstein manifolds. The higher-dimensional action has a cosmological term $\\Lambda$ and a $q$-form flux, which individually wraps each element of the product; the extended dimensions $M_p$ can be anti-de Sitter, Minkowski, or de Sitter. We find the masses of every excitation around this background, as well as the conditions under which these solutions are stable. This generalizes previous work on Freund-Rubin vacua, which focused on the $N=1$ case, in which a $q$-form flux wraps a single $q$-dimensional Einstein manifold. The $N=1$ case can have a classical instability when the $q$-dimensional internal manifold is a product---one of the members of the product wants to shrink while the rest of the manifold expands. Here, we will see that individually wrapping each element of the product with a lower-form flux cures this cycle-collapse instability. The $N=1$ case can also have an instability when $\\Lambda>0$ and $q\\ge4$ to shape-mode perturbations; we find the same instability in compactifications with general $N$, and show that it even extends to cases where $\\Lambda\\le0$. On the other hand, when $q=2$ or 3, the shape modes are always stable and there is a broad class of AdS and de Sitter vacua that are perturbatively stable to all fluctuations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-23T20:00:03.000Z",
      "comment": "51 pages, 4 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-23T00:25:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "04.50.-h",
      "95.30.Sf"
    ],
    "keywords": [
      "product manifolds",
      "dimensional einstein manifold",
      "instability",
      "dimensional internal manifold",
      "lower-form flux cures"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review D",
      "year": 2014,
      "month": "Aug",
      "volume": 90,
      "number": 4,
      "pages": "044047"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1262000,
      "adsabs": "2014PhRvD..90d4047B"
    }
  }
}