Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations
Abstract The integrability of the N=1 $$ \mathcal{N}=1 $$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such transformation is performed by using essentially tw...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP01(2018)018 |
| _version_ | 1819098431166087168 |
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| author | A.R. Aguirre A.L. Retore J.F. Gomes N.I. Spano A.H. Zimerman |
| author_facet | A.R. Aguirre A.L. Retore J.F. Gomes N.I. Spano A.H. Zimerman |
| author_sort | A.R. Aguirre |
| collection | DOAJ |
| description | Abstract The integrability of the N=1 $$ \mathcal{N}=1 $$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such transformation is performed by using essentially two methods: the Bäcklund-defect matrix approach and the superfield approach. Firstly, we employ the defect matrix associated to the hierarchy which turns out to be the same for the supersymmetric sinh-Gordon (sshG) model. The method is general for all flows and as an example we derive explicitly the Bäcklund equations in components for the first few flows of the hierarchy, namely t 3 and t 5. Secondly, the supersymmetric extension of the Bäcklund transformation in the superspace formalism is constructed for those flows. Finally, this super Bäcklund transformation is employed to introduce type I defects for the supersymmetric mKdV hierarchy. Further integrability aspects by considering modified conserved quantities are derived from the defect matrix. |
| first_indexed | 2024-12-22T00:30:52Z |
| format | Article |
| id | doaj.art-46a03670d62444fb852e10ea5ae4bc55 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T00:30:52Z |
| publishDate | 2018-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-46a03670d62444fb852e10ea5ae4bc552022-12-21T18:44:57ZengSpringerOpenJournal of High Energy Physics1029-84792018-01-012018113910.1007/JHEP01(2018)018Defects in the supersymmetric mKdV hierarchy via Bäcklund transformationsA.R. Aguirre0A.L. Retore1J.F. Gomes2N.I. Spano3A.H. Zimerman4Instituto de Física e Química, Universidade Federal de ItajubáInstituto de Física Teórica — UNESPInstituto de Física Teórica — UNESPInstituto de Física Teórica — UNESPInstituto de Física Teórica — UNESPAbstract The integrability of the N=1 $$ \mathcal{N}=1 $$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such transformation is performed by using essentially two methods: the Bäcklund-defect matrix approach and the superfield approach. Firstly, we employ the defect matrix associated to the hierarchy which turns out to be the same for the supersymmetric sinh-Gordon (sshG) model. The method is general for all flows and as an example we derive explicitly the Bäcklund equations in components for the first few flows of the hierarchy, namely t 3 and t 5. Secondly, the supersymmetric extension of the Bäcklund transformation in the superspace formalism is constructed for those flows. Finally, this super Bäcklund transformation is employed to introduce type I defects for the supersymmetric mKdV hierarchy. Further integrability aspects by considering modified conserved quantities are derived from the defect matrix.http://link.springer.com/article/10.1007/JHEP01(2018)018Integrable Field TheoriesIntegrable Hierarchies |
| spellingShingle | A.R. Aguirre A.L. Retore J.F. Gomes N.I. Spano A.H. Zimerman Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations Journal of High Energy Physics Integrable Field Theories Integrable Hierarchies |
| title | Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations |
| title_full | Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations |
| title_fullStr | Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations |
| title_full_unstemmed | Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations |
| title_short | Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations |
| title_sort | defects in the supersymmetric mkdv hierarchy via backlund transformations |
| topic | Integrable Field Theories Integrable Hierarchies |
| url | http://link.springer.com/article/10.1007/JHEP01(2018)018 |
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