  A manifestly gauge invariant and regularized renormalization group flow
equation is constructed for pure SU(N) gauge theory in the large N limit. In
this way we make precise and concrete the notion of a non-perturbative gauge
invariant continuum Wilsonian effective action. Manifestly gauge invariant
calculations may be performed, without gauge fixing, and receive a natural
interpretation in terms of fluctuating Wilson loops. Regularization is achieved
by covariant higher derivatives and by embedding in a spontaneously broken
SU(N|N) supergauge theory; the resulting heavy fermionic vectors are
Pauli-Villars fields. We prove the finiteness of this method to one loop and
any number of external gauge fields. A duality is uncovered that changes the
sign of the squared coupling constant. As a test of the basic formalism we
compute the one loop beta function, for the first time without any gauge
fixing, and prove its universality with respect to cutoff function.

High Energy Physics - Theory;Condensed Matter;High Energy Physics - Lattice;High Energy Physics - Phenomenology