Advancing real-time Yang-Mills: towards real-time observables from first principles

The complex Langevin (CL) method shows great promise in enabling the calculation of observables for theories with complex actions. Nevertheless, real-time quantum field theories have remained largely unsolved due to the particular severity of the sign problem. In this contribution, we discuss our recent progress in applying CL to a thermal SU(2) Yang-Mills theory on a 3+1 dimensional lattice. We present our anisotropic kernel that stabilizes the CL approach for real times longer than the inverse temperature - a first for Yang-Mills theory. We provide explicit evidence of reproducing symmetries and relations among different types of propagators when the complex time path approaches the Schwinger-Keldysh contour. This method paves the way for calculating transport coefficients and other real-time observables from first principles.