{
  "id": "2108.09330",
  "version": "v1",
  "published": "2021-08-20T18:43:59.000Z",
  "updated": "2021-08-20T18:43:59.000Z",
  "title": "Conformal Bootstrap with Reinforcement Learning",
  "authors": [
    "Gergely Kántor",
    "Vasilis Niarchos",
    "Constantinos Papageorgakis"
  ],
  "comment": "54 pages",
  "categories": [
    "hep-th"
  ],
  "abstract": "We introduce the use of reinforcement-learning (RL) techniques to the conformal-bootstrap programme. We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap high-dimensional searches in the space of scaling dimensions and OPE-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation. In this paper we test this approach in well-known 2D CFTs, with particular focus on the Ising and tri-critical Ising models and the free compactified boson CFT. We present results of as high as 36-dimensional searches, whose sole input is the expected number of operators per spin in a truncation of the conformal-block decomposition of the crossing equations. Our study of 2D CFTs uses only the global $so(2,2)$ part of the conformal algebra, and our methods are equally applicable to higher-dimensional CFTs. When combined with other, already available, numerical and analytical methods, we expect our approach to yield an exciting new window into the non-perturbative structure of arbitrary (unitary or non-unitary) CFTs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-20T18:43:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conformal bootstrap",
      "reinforcement learning",
      "suitable soft actor-critic rl algorithms",
      "free compactified boson cft",
      "well-known 2d cfts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}