A gauge invariant exact renormalization group II

A manifestly gauge invariant and regularized renormalization group flow equation is constructed for pure SU(N) gauge theory in the largeN 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 β function, for the first time without any gauge fixing, and prove its universality with respect to cutoff function. hep-th/0006064 June, 2000.