Manifestly gauge invariant exact renormalization group
We construct a manifestly gauge invariant Exact Renormalization Group for SU(N) YangMills theory, in a form suitable for calculations without gauge fixing at any order of perturbation theory. The effective cutoff is incorporated via a manifestly realised spontaneously broken SU(N|N) gauge invariance. Diagrammatic methods are developed which allow the calculations to proceed without specifying the precise form of the cutoff structure. We confirm consistency by computing for the first time both the one and two loop beta function coefficients without fixing the gauge or specifying the details of the cutoff. We conclude by sketching how quarks fit in and a new non-perturbative approximation scheme.