  We consider continuum formulation QCD in four dimensions with twelve massless
fundamental quark flavors. Splitting the SU(N) gauge field into background and
fluctuation parts, we use well developed techniques to calculate the one-loop
effective action for the theory. We find that for constant self-dual background
field-strength tensor the notorious infrared divergences of the effective
action cancel between gauge and matter sectors if the number of massless quark
flavors is exactly $N_f = 4N$. The ultraviolet divergencies of the effective
action are non-perturbatively renormalized with a $\beta$-function that matches
the known perturbative result in the weak coupling limit. The resulting UV- and
IR-finite effective action possesses a non-trivial minimum which has lower free
energy than the perturbative vacuum, and for which the expectation value of the
Polyakov loop vanishes. Inclusion of finite temperature effects points to the
presence of a first-order phase transition to the perturbative vacuum with a
calculable critical temperature.
