{
  "id": "2405.04076",
  "version": "v1",
  "published": "2024-05-07T07:20:47.000Z",
  "updated": "2024-05-07T07:20:47.000Z",
  "title": "2d Sinh-Gordon model on the infinite cylinder",
  "authors": [
    "Colin Guillarmou",
    "Trishen S. Gunaratnam",
    "Vincent Vargas"
  ],
  "comment": "35 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For $R>0$, we give a rigorous probabilistic construction on the cylinder $\\mathbb{R} \\times (\\mathbb{R}/(2\\pi R\\mathbb{Z}))$ of the (massless) Sinh-Gordon model. In particular we define the $n$-point correlation functions of the model and show that these exhibit a scaling relation with respect to $R$. The construction, which relies on the massless Gaussian Free Field, is based on the spectral analysis of a quantum operator associated to the model. Using the theory of Gaussian multiplicative chaos, we prove that this operator has discrete spectrum and a strictly positive ground state.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-07T07:20:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "81T40"
    ],
    "keywords": [
      "2d sinh-gordon model",
      "infinite cylinder",
      "massless gaussian free field",
      "point correlation functions",
      "rigorous probabilistic construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}