Strongly coupled QFT dynamics via TQFT coupling

Abstract 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[−8π 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 × S L 1 $$ {S}_L^1 $$ 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 θ = 0 and gaplessness at θ = π in CP $$ \mathbbm{CP} $$ 1 model, and mass gap for arbitrary θ in CP $$ \mathbbm{CP} $$ N−1 , N ≥ 3 on ℝ2