Manifestly Gauge Invariant QCD

TL;DR

This paper develops a gauge-invariant exact renormalization group framework for QCD by embedding it in a spontaneously broken SU(N|N) gauge theory, enabling calculations like the one-loop beta function without gauge fixing.

Contribution

It introduces a novel gauge-invariant regularization method for QCD using SU(N|N) embedding and covariant higher derivatives, improving computational efficiency.

Findings

Constructed a gauge-invariant cutoff via SU(N|N) embedding.

Achieved a universal one-loop beta function calculation without gauge fixing.

Demonstrated the formalism's efficiency when flavors are multiples of colors.

Abstract

Building on recent work in SU(N) Yang-Mills theory, we construct a manifestly gauge invariant exact renormalization group for QCD. A gauge invariant cutoff 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 beta function, achieving a manifestly universal result and without fixing the gauge.