  We propose a 5-dimensional definition for the physical 4D-Yang-Mills theory.
The fifth dimension corresponds to the Monte-Carlo time of numerical
simulations of QCD_4. The 5-dimensional theory is a well-defined topological
quantum field theory that can be renormalized at any given finite order of
perturbation theory. The relation to non-perturbative physics is obtained by
expressing the theory on a lattice, a la Wilson. The new fields that must be
introduced in the context of a topological Yang-Mills theory have a simple
lattice expression. We present a 5-dimensional critical limit for physical
correlation functions and for dynamical auto-correlations, which allows new
Monte-Carlo algorithm based on the time-step in lattice units given by $\e =
g_0^{-13/11}$ in pure gluodynamics. The gauge-fixing in five dimensions is such
that no Gribov ambiguity occurs. The weight is strictly positive, because all
ghost fields have parabolic propagators and yield trivial determinants. We
indicate how our 5-dimensional description of the Yang-Mills theory may be
extended to fermions.
