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 glo...

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Autor principal:	Mithat Ünsal
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Confinement Sigma Models Solitons Monopoles and Instantons Topological Field Theories Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/0d98fc362d804a9b80598b3365f34a4a
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spelling	oai:doaj.org-article:0d98fc362d804a9b80598b3365f34a4a2021-11-28T12:40:41ZStrongly coupled QFT dynamics via TQFT coupling10.1007/JHEP11(2021)1341029-8479https://doaj.org/article/0d98fc362d804a9b80598b3365f34a4a2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)134https://doaj.org/toc/1029-8479Abstract 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.Mithat ÜnsalSpringerOpenarticleConfinementSigma ModelsSolitons Monopoles and InstantonsTopological Field TheoriesNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-88 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Confinement Sigma Models Solitons Monopoles and Instantons Topological Field Theories Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Confinement Sigma Models Solitons Monopoles and Instantons Topological Field Theories Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Mithat Ünsal Strongly coupled QFT dynamics via TQFT coupling
description	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.
format	article
author	Mithat Ünsal
author_facet	Mithat Ünsal
author_sort	Mithat Ünsal
title	Strongly coupled QFT dynamics via TQFT coupling
title_short	Strongly coupled QFT dynamics via TQFT coupling
title_full	Strongly coupled QFT dynamics via TQFT coupling
title_fullStr	Strongly coupled QFT dynamics via TQFT coupling
title_full_unstemmed	Strongly coupled QFT dynamics via TQFT coupling
title_sort	strongly coupled qft dynamics via tqft coupling
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/0d98fc362d804a9b80598b3365f34a4a
work_keys_str_mv	AT mithatunsal stronglycoupledqftdynamicsviatqftcoupling
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Strongly coupled QFT dynamics via TQFT coupling

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