Towards a manifestly gauge invariant and universal calculus for Yang-Mills theory

Abstract

A manifestly gauge invariant exact renormalization group for pure SU(N) Yang-Mills theory is proposed, along with the necessary gauge invariant regularisation which implements the effective cutoff. The latter is naturally incorporated by embedding the theory into a spontaneously broken SU(N|N) super-gauge theory, which guarantees finiteness to all orders in perturbation theory. The effective action, from which one extracts the physics, can be computed whilst manifestly preserving gauge invariance at each and every step. As an example, we give an elegant computation of the one-loop SU(N) Yang-Mills beta function, for the first time at finite N without any gauge fixing or ghosts. It is also completely independent of the details put in by hand, e.g. the choice of covariantisation and the cutoff profile, and, therefore, guides us to a procedure for streamlined calculations.