N=4 Multi-Particle Mechanics, WDVV Equation and Roots
We review the relation of N=4 superconformal multi-particle models on the real line to the WDVV equation and an associated linear equation for two prepotentials, F and U. The superspace treatment gives another variant of the integrability problem, which we also reformulate as a search for closed fla...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146796 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | N=4 Multi-Particle Mechanics, WDVV Equation and Roots / O. Lechtenfeld, K. Schwerdtfeger, J. Thürigen // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 35 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862701020039086080 |
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| author | Lechtenfeld, O. Schwerdtfeger, K. Thürigen, J. |
| author_facet | Lechtenfeld, O. Schwerdtfeger, K. Thürigen, J. |
| citation_txt | N=4 Multi-Particle Mechanics, WDVV Equation and Roots / O. Lechtenfeld, K. Schwerdtfeger, J. Thürigen // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 35 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review the relation of N=4 superconformal multi-particle models on the real line to the WDVV equation and an associated linear equation for two prepotentials, F and U. The superspace treatment gives another variant of the integrability problem, which we also reformulate as a search for closed flat Yang-Mills connections. Three- and four-particle solutions are presented. The covector ansatz turns the WDVV equation into an algebraic condition, for which we give a formulation in terms of partial isometries. Three ideas for classifying WDVV solutions are developed: ortho-polytopes, hypergraphs, and matroids. Various examples and counterexamples are displayed.
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| first_indexed | 2025-12-07T16:40:45Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146796 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:40:45Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lechtenfeld, O. Schwerdtfeger, K. Thürigen, J. 2019-02-11T15:22:02Z 2019-02-11T15:22:02Z 2011 N=4 Multi-Particle Mechanics, WDVV Equation and Roots / O. Lechtenfeld, K. Schwerdtfeger, J. Thürigen // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 35 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70E55; 81Q60; 17B22; 52B40; 05C65 DOI:10.3842/SIGMA.2011.023 https://nasplib.isofts.kiev.ua/handle/123456789/146796 We review the relation of N=4 superconformal multi-particle models on the real line to the WDVV equation and an associated linear equation for two prepotentials, F and U. The superspace treatment gives another variant of the integrability problem, which we also reformulate as a search for closed flat Yang-Mills connections. Three- and four-particle solutions are presented. The covector ansatz turns the WDVV equation into an algebraic condition, for which we give a formulation in terms of partial isometries. Three ideas for classifying WDVV solutions are developed: ortho-polytopes, hypergraphs, and matroids. Various examples and counterexamples are displayed. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 The authors are grateful to Martin Rubey for pointing them to and helping them with hypergraphs and matroids. Of course, all mistakes are ours! O.L. acknowledges fruitful discussions with Misha Feigin, Evgeny Ivanov, Sergey Krivonos, Andrei Smilga and Sasha Veselov. He also thanks the organizers of the Benasque workshop for a wonderful job. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications N=4 Multi-Particle Mechanics, WDVV Equation and Roots Article published earlier |
| spellingShingle | N=4 Multi-Particle Mechanics, WDVV Equation and Roots Lechtenfeld, O. Schwerdtfeger, K. Thürigen, J. |
| title | N=4 Multi-Particle Mechanics, WDVV Equation and Roots |
| title_full | N=4 Multi-Particle Mechanics, WDVV Equation and Roots |
| title_fullStr | N=4 Multi-Particle Mechanics, WDVV Equation and Roots |
| title_full_unstemmed | N=4 Multi-Particle Mechanics, WDVV Equation and Roots |
| title_short | N=4 Multi-Particle Mechanics, WDVV Equation and Roots |
| title_sort | n=4 multi-particle mechanics, wdvv equation and roots |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146796 |
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