Complex Langevin Simulations of Supersymmetric Theories

Abstract: This review explores the Complex Langevin Method (CLM), a stochastic quantization technique designed to address the sign problem in quantum field theories with complex actions. Beginning with foundational principles, the review examines the applications of CLM across a range of models, including zero- and two-dimensional systems, supersymmetric quantum mechanics, and the IKKT matrix model, a candidate for non-perturbative string theory. Key advancements, such as stabilization techniques and mass deformations, are highlighted as solutions to challenges like numerical instability and singular drift terms. The review emphasizes the capacity of CLM to simulate complex systems and reveal non-perturbative phenomena, positioning it as a powerful tool for exploring quantum field theory and string theory. Future directions, including higher-dimensional applications and benchmarking against quantum simulations, underscore the potential of CLM to advance both theoretical understanding and computational methodologies.