Status of Complex Langevin

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.