A gauge invariant exact renormalization group II

A manifestly gauge invariant and regularized renormalization group ow equat ion is constructed for pure SU(N) gauge theory in the large-N limit. In thi s way we make precise and concrete the notion of a non-perturbative gauge i nvariant continuum wilsonian effective action. Manifestly gauge invariant c alculations may be performed, without gauge fixing, and receive a natural i nterpretation in terms of fluctuating Wilson loops. Regularization is achie ved by covariant higher derivatives and by embedding in a spontaneously bro ken SU(N\N) supergauge theory; the resulting heavy fermionic vectors are Pa uli-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 th e sign of the squared coupling constant. As a test of the basic formalism w e compute the one loop beta function, for the first time without any gauge fixing, and prove its universality with respect to cutoff function.