  We study the stochastic cubic complex Ginzburg-Landau equation with
complex-valued space-time white noise on the three dimensional torus. This
nonlinear equation is so singular that it can only be under- stood in a
renormalized sense. In the first half of this paper we prove local
well-posedness of this equation in the framework of regularity structure
theory. In the latter half we prove local well-posedness in the framework of
paracontrolled distribution theory.
