Manifestly gauge-invariant QCD

Building on recent work in SU(N) Yang–Mills theory, we construct a manifestly gauge-invariant exact renormalization group for QCD. A gauge-invariant cut-off is constructed by embedding the physical gauge theory in a spontaneously broken SU(N|N) gauge theory, regularized by covariant higher derivatives. Intriguingly, the construction is most efficient if the number of flavours is a multiple of the number of colours. The formalism is illustrated with a very compact calculation of the one-loop β-function, achieving a manifestly universal result and without fixing the gauge.