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.
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