{
  "id": "2111.12716",
  "version": "v3",
  "published": "2021-11-24T19:00:01.000Z",
  "updated": "2024-01-21T20:59:26.000Z",
  "title": "Automorphic Spectra and the Conformal Bootstrap",
  "authors": [
    "Petr Kravchuk",
    "Dalimil Mazac",
    "Sridip Pal"
  ],
  "comment": "v2: various improvements, especially in Section 3.9; v3: published version",
  "journal": "Comm. Amer. Math. Soc. 4 (2024), 1-63",
  "doi": "10.1090/cams/26",
  "categories": [
    "hep-th",
    "math-ph",
    "math.MP",
    "math.RT",
    "math.SP"
  ],
  "abstract": "We describe a new method for constraining Laplacian spectra of hyperbolic surfaces and 2-orbifolds. The main ingredient is consistency of the spectral decomposition of integrals of products of four automorphic forms. Using a combination of representation theory of $\\mathrm{PSL}_2(\\mathbb{R})$ and semi-definite programming, the method yields rigorous upper bounds on the Laplacian spectral gap. In several examples, the bound is nearly sharp. For instance, our bound on all genus-2 surfaces is $\\lambda_1\\leq 3.8388976481$, while the Bolza surface has $\\lambda_1\\approx 3.838887258$. The bounds also allow us to determine the set of spectral gaps attained by all hyperbolic 2-orbifolds. Our methods can be generalized to higher-dimensional hyperbolic manifolds and to yield stronger bounds in the two-dimensional case. The ideas were closely inspired by modern conformal bootstrap.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2024-01-21T20:59:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "11F70",
      "43A85",
      "81T05",
      "58C40"
    ],
    "keywords": [
      "conformal bootstrap",
      "automorphic spectra",
      "method yields rigorous upper bounds",
      "higher-dimensional hyperbolic manifolds",
      "yield stronger bounds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}