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Solving Conformal Field Theories with Artificial Intelligence.

Gergely Kántor1, Constantinos Papageorgakis1, Vasilis Niarchos2

  • 1Centre for Theoretical Physics, Department of Physics and Astronomy Queen Mary University of London, London E1 4NS, United Kingdom.

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This study introduces reinforcement learning for solving conformal field theories (CFTs) via the conformal bootstrap. Researchers successfully identified models like the 2D Ising model, demonstrating a new method for exploring complex CFTs.

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Area of Science:

  • Theoretical Physics
  • Computational Physics

Background:

  • Conformal Field Theories (CFTs) are crucial in understanding critical phenomena and quantum gravity.
  • The conformal bootstrap program provides a powerful, albeit computationally intensive, framework for studying CFTs.
  • Numerical solutions are essential for exploring CFTs that lack analytical solutions.

Purpose of the Study:

  • To develop and apply novel computational methods for solving CFTs.
  • To leverage reinforcement learning algorithms within the conformal bootstrap program.
  • To demonstrate the efficacy of these methods on known 2D CFTs.

Main Methods:

  • Implementation of reinforcement-learning algorithms, specifically a soft actor-critic algorithm.
  • Application to truncated crossing equations in two-dimensional CFTs.
  • Utilizing high-dimensional search capabilities for arbitrary CFTs.

Main Results:

  • Obtained approximate numerical solutions for 2D CFTs.
  • Successfully identified the 2D Ising model and a 2D CFT of a compactified scalar.
  • Demonstrated the efficiency of the method in high-dimensional searches.

Conclusions:

  • Reinforcement learning offers a viable and efficient approach for numerical solutions in CFTs.
  • The developed methods are applicable to a wide range of CFTs, including unitary and nonunitary theories in any dimension.
  • This work opens new avenues for exploring complex theoretical physics models computationally.