Strongly coupled $$\mathrm{QFT}$$ dynamics via $$\mathrm{TQFT}$$ coupling
Abstract
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[-SI/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.
- Authors:
-
- North Carolina State University, Raleigh, NC (United States)
- Publication Date:
- Research Org.:
- North Carolina State University, Raleigh, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1976581
- Grant/Contract Number:
- SC0013036
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 11; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; confinement; sigma models; solitons monopoles and instantons; topological field theories
Citation Formats
Ünsal, Mithat. Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling. United States: N. p., 2021.
Web. doi:10.1007/jhep11(2021)134.
Ünsal, Mithat. Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling. United States. https://doi.org/10.1007/jhep11(2021)134
Ünsal, Mithat. Thu .
"Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling". United States. https://doi.org/10.1007/jhep11(2021)134. https://www.osti.gov/servlets/purl/1976581.
@article{osti_1976581,
title = {Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling},
author = {Ünsal, Mithat},
abstractNote = {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[-SI/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.},
doi = {10.1007/jhep11(2021)134},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2021,
place = {United States},
year = {Thu Nov 18 00:00:00 EST 2021},
month = {Thu Nov 18 00:00:00 EST 2021}
}
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