  The complex Langevin (CL) method is a promising approach to overcome the sign
problem that occurs in real-time formulations of quantum field theories. Using
the Schwinger-Keldysh formalism, we study SU($N_c$) gauge theories with CL. We
observe that current stabilization techniques are insufficient to obtain
correct results. Therefore, we revise the discretization of the CL equations on
complex time contours, find a time reflection symmetric formulation and
introduce a novel anisotropic kernel that enables CL simulations on discretized
complex time paths. Applying it to SU(2) Yang-Mills theory in 3+1 dimensions,
we obtain unprecedentedly stable results that we validate using additional
observables and that can be systematically improved. For the first time, we are
able to simulate non-Abelian gauge theory on time contours whose real-time
extent exceeds its inverse temperature. Thus, our approach may pave the way
towards an ab-initio real-time framework of QCD in and out of equilibrium with
a potentially large impact on the phenomenology of heavy-ion collisions.

High Energy Physics - Lattice;High Energy Physics - Phenomenology