# High Energy Theory Seminar

Friday, July 17, 2020
11:00am to 12:00pm
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 global symmetry.In  SU(N)  Yang-Mills theory  coupled to  $\mathbb Z_N$ TQFT,   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  and action 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, providing a TQFT protected generalization of resurgent semiclassical expansion to strong coupling.  Monopole-instantons (or fractional instantons) on $T^3 \times S^1_L$  can be interpreted as tunneling events in the 't Hooft flux background  in the $PSU(N)$ bundle.  The  construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between  the large-$N$ and  instanton analysis.  If time permits, I will give a self-consistent derivation of the mass gap as a function of theta angle in $CP^{N-1}$ theory.