Conformal Bootstrap with Reinforcement Learning
| Autor: | Kántor, Gergely, Niarchos, Vasilis, Papageorgakis, Constantinos |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.105.025018 |
| Popis: | 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. Comment: 54 pages; v2: typos corrected and references added; v3: minor corrections |
| Databáze: | arXiv |
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