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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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP11(2021)134 |
| _version_ | 1818342209479507968 |
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| author | Mithat Ünsal |
| author_facet | Mithat Ünsal |
| author_sort | Mithat Ünsal |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-13T16:11:03Z |
| format | Article |
| id | doaj.art-0d98fc362d804a9b80598b3365f34a4a |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T16:11:03Z |
| publishDate | 2021-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-0d98fc362d804a9b80598b3365f34a4a2022-12-21T23:38:56ZengSpringerOpenJournal of High Energy Physics1029-84792021-11-0120211118810.1007/JHEP11(2021)134Strongly coupled QFT dynamics via TQFT couplingMithat Ünsal0Department of Physics, North Carolina State UniversityAbstract 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.https://doi.org/10.1007/JHEP11(2021)134ConfinementSigma ModelsSolitons Monopoles and InstantonsTopological Field Theories |
| spellingShingle | Mithat Ünsal Strongly coupled QFT dynamics via TQFT coupling Journal of High Energy Physics Confinement Sigma Models Solitons Monopoles and Instantons Topological Field Theories |
| title | 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_short | Strongly coupled QFT dynamics via TQFT coupling |
| title_sort | strongly coupled qft dynamics via tqft coupling |
| topic | Confinement Sigma Models Solitons Monopoles and Instantons Topological Field Theories |
| url | https://doi.org/10.1007/JHEP11(2021)134 |
| work_keys_str_mv | AT mithatunsal stronglycoupledqftdynamicsviatqftcoupling |