Complex Langevin simulations for PT-symmetric models

Abstract

Self-interacting scalar quantum field theories possessing 𝑃𝑇-symmetry are physically admissible since their energy spectrum is real and bounded below. However, models with 𝑃𝑇-invariant potentials can have complex actions in general and a non-perturbative study of such systems using methods based on traditional Monte Carlo is hindered due to numerical sign problem. In this work we employ complex Langevin based on stochastic quantization to study two-dimensional scalar field theories, including the ones exhibiting 𝑃𝑇-symmetry. We also study the simplest supersymmetric version of these systems and address the question on dynamical supersymmetry breaking.