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 semiclassical 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 P SU (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 1 L can be interpreted as tunneling events in the 't Hooft flux background in the P SU (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 1 model, and mass gap for arbitrary θ in CP N −1 , N ≥ 3 on R 2 .

Exact-WKB analysis for SUSY and quantum deformed potentials: Quantum mechanics with Grassmann fields and Wess-Zumino terms

“…Furthermore, we now understand that there are compactification of QFTs with 't Hooft fluxes to QM systems which preserve various anomalies and non-perturbative saddle points, see eg. [63]. In these theories, integrating out fermions in a weak coupling calculable regime induces an O( ) deformation to classical action, similar to our quantum deformed system.…”

Notes on Confinement on $\mathbf{R^3 \times S^1}$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)

“…It should be stressed that, at the moment, we do not have a rigorous argument favouring (130) or (131). For recent discussions showing the consistency of this scenario with various anomalies, see [107,113,114,115,116], while [98] has the most recent lattice results, unfortunately not yet decisive.…”

“…20. We also discussed two possible scenarios for the behaviour of the n f = 2, 3, ... theory in the R 4 limit, one with a SU (n f )-breaking phase transition upon increase of L, with a nonvanishing bilinear condensate (130), and the other obeying "adiabatic continuity," with the multifermion condensate of ( 131) and an unbroken SU (n f ) on R 4 . the small-L SYM also becomes weakly-coupled and semiclassically calculable (provided the S 1 holonomy is near the middle of the Weyl chamber of Fig.…”

“…We shall argue that necessity of analytic continuation in different quantum mechanics examples. See also the recent proposals [130,125,44] relating the quantum mechanical and QFT discussions.…”

“…The appendix of the latter reference has a physicist-friendly discussion of the gauging of the 1-form center symmetry for all gauge groups on the four-torus, relevant for the 't Hooft anomaly between center symmetry and parity or discrete chiral symmetry. Further related recent work is in [130,125].…”