High Energy / Nuclear Theory / RIKEN seminars

[virtual NT/RIKEN seminar] Strongly coupled QFT dynamics via TQFT coupling

by Mithat Unsal (NCSU)




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.