{
  "id": "2312.13337",
  "version": "v1",
  "published": "2023-12-20T19:00:00.000Z",
  "updated": "2023-12-20T19:00:00.000Z",
  "title": "Conformal Perturbation Theory for $n$-Point Functions: Structure Constant Deformation",
  "authors": [
    "Benjamin A. Burrington",
    "Ida G. Zadeh"
  ],
  "comment": "34 pp + appendices, 3 figures",
  "categories": [
    "hep-th"
  ],
  "abstract": "We consider conformal perturbation theory for $n$-point functions on the sphere in general 2D CFTs to first order in coupling constant. We regulate perturbation integrals using canonical hard disk excisions of size $\\epsilon$ around the fixed operator insertions, and identify the full set of counter terms which are sufficient to regulate all such integrated $n$-point functions. We further explore the integrated 4-point function which computes changes to the structure constants of the theory. Using an $sl(2)$ map, the three fixed locations of operators are mapped to $0$, $1$, and $\\infty$. We show that approximating the mapped excised regions to leading order in $\\epsilon$ does not lead to the same perturbative shift to the structure constant as the exact in $\\epsilon$ region. We explicitly compute the correction back to the exact in $\\epsilon$ region of integration in terms of the CFT data. We consider the compact boson, and show that one must use the exact in $\\epsilon$ region to obtain agreement with the exact results for structure constants in this theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-20T19:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal perturbation theory",
      "point functions",
      "structure constant deformation",
      "general 2d cfts",
      "canonical hard disk excisions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}