virtual NT/RIKEN seminar

We consider a class of quantum field theories and quantum mechanics, which we couple to topological QFTs, in order to classify non-perturbative effects in the original theory. The TQFT structure arises naturally from turning on a classical background field for a discrete 0- or 1-form global symmetry present in the theory. By using this method, I prove that the the non-perturbative expansion parameter is exp[-S_I/N]= \exp[-{8 \pi^2}/{g^2N}], both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute.