Strongly coupled QFT dynamics via TQFT coupling

We consider a class of quantum field theories and quantum mechanics, which we couple to Z(N) topological QFTs, in order to classify non-perturbative effects in the original theory. The Z(N) TQFT structure arises naturally from turning on a classical background field for a Z(N) 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to Z(N) TQFT, the non-perturbative expansion parameter is exp[-S-I/N] = exp[-8 pi(2)/g(2)N] 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, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T-3 x S-L(1) 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. We derive the mass gap at theta = 0 and gaplessness at ;theta = pi in CP1 model, and mass gap for arbitrary theta in CPN-1, N >= 3 on R-2.

Automated summary

The paper discusses a class of quantum field theories and quantum mechanics, coupled with Z(N) topological QFTs to classify non-perturbative effects in the original theory. The coupling of SU(N) Yang-Mills theory with Z(N) TQFT and the importance of PSU(N) bundle and lift configurations are highlighted, providing a new perspective and solutions for the strong coupling regime.