  We introduce new variables in four dimensional SU(N) Yang-Mills theory. These
variables emerge when we sum the path integral over classical solutions and
represent the summation as an integral over appropriate degrees of freedom. In
this way we get an effective field theory with SU(N)$\times$SU(N) gauge
symmetry. In the instanton approximation our effective theory has in addition a
N=2 supersymmetry, and when we sum over all possible solutions we find a
Parisi-Sourlas supersymmetry. These extra symmetries can then be broken
explicitly by a SU(N) invariant and power counting renormalizable mass term.
Our results suggest that the confinement mechanism which has been recently
identified in the N=2 supersymmetric Yang-Mills theory might also help to
understand color confinement in ordinary, pure Yang-Mills theory. In
particular, there appears to be an intimate relationship between the N=2
supersymmetry approach to confinement and the Parisi-Sourlas dimensional
reduction.
