Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling

Ünsal, Mithat

doi:10.1007/jhep11(2021)134

Title: Strongly coupled $$\mathrm{QFT}$$ dynamics via $$\mathrm{TQFT}$$ coupling

Journal Article · Thu Nov 18 00:00:00 EST 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep11(2021)134· OSTI ID:1976581

Ünsal, Mithat ^[1]

North Carolina State University, Raleigh, NC (United States)

We consider a class of quantum field theories and quantum mechanics, which we couple to $$\mathbb{Z}$$_N topological QFTs, in order to classify non-perturbative effects in the original theory. The $$\mathbb{Z}$$_N TQFT structure arises naturally from turning on a classical background field for a $$\mathbb{Z}$$_N 0- or 1-form 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[-8π²/g²N] 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 T³ x $$S^1_L$$ 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. We derive the mass gap at θ = 0 and gaplessness at θ = π in $$\mathbb{CP}$$¹ model, and mass gap for arbitrary θ in $$\mathbb{CP}$$ ^N-1, N ≥ 3 on $$\mathbb{R}$$².

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Research Organization:: North Carolina State University, Raleigh, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0013036

OSTI ID:: 1976581

Journal Information:: Journal of High Energy Physics (Online), Vol. 2021, Issue 11; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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