A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory

Abstract

We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularization scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. The initial stages can even be computed diagrammatically. The method is formulated within the framework of an exact renormalization group for $\mathrm{SU}(N)$ Yang-Mills gauge theory, incorporating an effective cutoff through a manifest spontaneously broken $\mathrm{SU}(N|N)$ gauge invariance. We demonstrate the technique with a compact calculation of the one-loop beta function, achieving a manifestly universal result, and without gauge fixing, for the first time at finite N.