Aspects of SU(Nc) gauge theories in the limit of small number of colors

We investigate properties of the color space of SU(Nc) gauge theories in the limit of small number of colors (Nc→0) and large number of flavors. More generally, we introduce a rescaling of αs and nf which assigns a finite limit to colored quantities as Nc→0, which reproduces their known large-Nc limit, and which expresses them as an analytic function of Nc2 for arbitrary value of Nc. The vanishing-Nc limit has an Abelian character and is also the small-Nc limit of [U(1)]Nc−1. This limit does not have an obvious quantum field theory interpretation; however, it provides practical consistency checks on QCD perturbative quantities by comparing them to their QED counterparts. Our analysis also describes the two-dimensional topological structure involved in the interpretation of the small Nc-limit in color space.