{
  "id": "1810.00840",
  "version": "v1",
  "published": "2018-10-01T17:31:41.000Z",
  "updated": "2018-10-01T17:31:41.000Z",
  "title": "Universality of Toda equation in ${\\cal N}=2$ superconformal field theories",
  "authors": [
    "Antoine Bourget",
    "Diego Rodriguez-Gomez",
    "Jorge G. Russo"
  ],
  "comment": "22 pages, no figures",
  "categories": [
    "hep-th"
  ],
  "abstract": "We show that extremal correlators in all Lagrangian ${\\cal N}=2$ superconformal field theories with a simple gauge group are governed by the same universal Toda system of equations, which dictates the structure of extremal correlators to all orders in the perturbation series. A key point is the construction of a convenient orthogonal basis for the chiral ring, by arranging towers of operators in order of increasing dimension, which has the property that the associated two-point functions satisfy decoupled Toda chain equations. We explicitly verify this in all known SCFTs based on $\\mathrm{SU}(N)$ gauge groups as well as in superconformal QCD based on orthogonal and symplectic groups. As a by-product, we find a surprising non-renormalization property for the ${\\cal N}=2$ $\\mathrm{SU}(N)$ SCFT with one hypermultiplet in the rank-2 symmetric representation and one hypermultiplet in the rank-2 antisymmetric representation, where the two-loop terms of a large class of supersymmetric observables identically vanish.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-01T17:31:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "superconformal field theories",
      "toda equation",
      "decoupled toda chain equations",
      "functions satisfy decoupled toda chain",
      "extremal correlators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}