I discuss the dynamics of four dimensional gauge theories with adjoint fermions for general gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena, and new instanton effects. I will describe whether we can actually make sense of gauge theory in continuum. In compactified theory, I will give evidence that the elusive IR renormalons (for which no semi-classical configuration is known) of 't Hooft may have a semi-classical incarnation.

This is a molecule that Argyres and I refer to as "neutral bion". It carries zero topological charge and zero magnetic charge, and it corresponds to a pole in the Borel plane much closer to origin (by a factor of N) than the 4d instanton-anti-instanton pole. We recently derived this class of molecules by generalizing an old work of Bogomolny and Zinn-Justin from quantum mechanics to quantum field theory. I suspect we may have a chance to understand this theory in continuum.