Going with the flow: a solution to the sign problem

​The Monte Carlo method is a robust way to study strongly interacting field theories and many body systems. However, the sign problem prevents its application to an important set of problems such as most field theories at finite density, as well as computation of real time quantities like transport coefficients. I will discuss an approach based on deforming the region of integration in the path integral into a complex manifold. This approach provides a way to mitigate the sign problem so that the Monte Carlo simulations can be profitably performed.
It also generalizes the "Lefschetz thimble" method which has gained attention recently. I will explain the idea in simple geometric terms, then introduce an algorithm that utilizes it and, finally, give examples of various models ranging from 0+1d fermionic systems to 3+1d relativistic Bose gas with nonzero chemical potential and real time dynamics.