Diagrammatic analysis of duality in supersymmetric gauge theories

We introduce a diagrammatic notation for supersymmetric gauge theories. The notation is a tool for exploring duality and helps to present the field content of more complicated models in a simple visual way. We introduce the notation with a few examples from the literature. The power of the formalism allows us to study models with gauge group $\left[\mathrm{SU}\mathrm{}\right(N)\mathrm{}{]}^k$ and their duals. Among these are models which, contrary to a naive analysis, possess no conformal phase.