Complex Langevin simulations for $PT$-symmetric models

TL;DR

This paper uses complex Langevin stochastic quantization to study two-dimensional $PT$-symmetric scalar field theories and their supersymmetric versions, overcoming the sign problem in non-perturbative analysis.

Contribution

It introduces the application of complex Langevin methods to $PT$-symmetric quantum field theories and explores supersymmetry breaking in these models.

Findings

Successful non-perturbative simulations of $PT$-symmetric models.

Evidence of dynamical supersymmetry breaking in the studied systems.

Validation of complex Langevin approach for complex actions.

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.