TL;DR
This paper reviews the Complex Langevin method, discussing its mathematical basis, limitations, and recent progress in applying it to QCD to explore its phase diagram under different conditions.
Contribution
It provides a comprehensive overview of the method's current status, including justification, challenges, and recent advancements in QCD applications.
Findings
Discussion of mathematical justification and limitations
Description of pragmatic measures for problem mitigation
Progress report on applying the method to QCD phase diagram
Abstract
I review the status of the Complex Langevin method, which was invented to make simulations of models with complex action feasible. I discuss the mathematical justification of the procedure, as well as its limitations and open questions. Various pragmatic measures for dealing with the existing problems are described. Finally I report on the progress in the application of the method to QCD, with the goal of determining the phase diagram of QCD as a function of temperature and baryonic chemical potential.
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