Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 models
Abstract We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂP N − 1 sigma model on ℝ×S 1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP02(2019)190 |
| _version_ | 1818284987998273536 |
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| author | Toshiaki Fujimori Syo Kamata Tatsuhiro Misumi Muneto Nitta Norisuke Sakai |
| author_facet | Toshiaki Fujimori Syo Kamata Tatsuhiro Misumi Muneto Nitta Norisuke Sakai |
| author_sort | Toshiaki Fujimori |
| collection | DOAJ |
| description | Abstract We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂP N − 1 sigma model on ℝ×S 1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the ℂP N − 1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon. |
| first_indexed | 2024-12-13T01:01:32Z |
| format | Article |
| id | doaj.art-87b61dd012cb4710919c5ae38110bd8b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T01:01:32Z |
| publishDate | 2019-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-87b61dd012cb4710919c5ae38110bd8b2022-12-22T00:04:39ZengSpringerOpenJournal of High Energy Physics1029-84792019-02-012019214110.1007/JHEP02(2019)190Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 modelsToshiaki Fujimori0Syo Kamata1Tatsuhiro Misumi2Muneto Nitta3Norisuke Sakai4Department of Physics, and Research and Education Center for Natural Sciences, Keio UniversityDepartment of Physics, North Carolina State UniversityDepartment of Physics, and Research and Education Center for Natural Sciences, Keio UniversityDepartment of Physics, and Research and Education Center for Natural Sciences, Keio UniversityDepartment of Physics, and Research and Education Center for Natural Sciences, Keio UniversityAbstract We derive the semiclassical contributions from the real and complex bions in the two-dimensional ℂP N − 1 sigma model on ℝ×S 1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the ℂP N − 1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon.http://link.springer.com/article/10.1007/JHEP02(2019)190Nonperturbative EffectsRenormalization Regularization and RenormalonsSigma Models |
| spellingShingle | Toshiaki Fujimori Syo Kamata Tatsuhiro Misumi Muneto Nitta Norisuke Sakai Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 models Journal of High Energy Physics Nonperturbative Effects Renormalization Regularization and Renormalons Sigma Models |
| title | Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 models |
| title_full | Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 models |
| title_fullStr | Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 models |
| title_full_unstemmed | Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 models |
| title_short | Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂP N − 1 models |
| title_sort | bion non perturbative contributions versus infrared renormalons in two dimensional cp n 1 models |
| topic | Nonperturbative Effects Renormalization Regularization and Renormalons Sigma Models |
| url | http://link.springer.com/article/10.1007/JHEP02(2019)190 |
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