Parton distributions of gluons in different representations

Abstract

It has been questioned if gluon distributions defined in different representations of $SU\left(N\right)$ are the same. The question has arisen in the connection to the recently proposed resolution of the so-called axial gauge puzzle. We give a proof that gluon distributions defined in the fundamental- and adjoint representations, where gauge links consist of those which are all future-pointing or all past-pointing, are the same. These gauge links are needed to make the distributions gauge invariant. When these links consist of not only future-pointing gauge links but also past-pointing ones, the puzzle appears. We examine the puzzle for distributions at one-loop in the cases with gauge links along time-like-, space-like- and light-cone direction.