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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2011 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146796 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146796 |
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dspace |
| spelling |
irk-123456789-1467962019-02-12T01:23:49Z N=4 Multi-Particle Mechanics, WDVV Equation and Roots Lechtenfeld, O. Schwerdtfeger, K. Thürigen, J. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146796 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Lechtenfeld, O. Schwerdtfeger, K. Thürigen, J. |
| spellingShingle |
Lechtenfeld, O. Schwerdtfeger, K. Thürigen, J. N=4 Multi-Particle Mechanics, WDVV Equation and Roots Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Lechtenfeld, O. Schwerdtfeger, K. Thürigen, J. |
| author_sort |
Lechtenfeld, O. |
| title |
N=4 Multi-Particle Mechanics, WDVV Equation and Roots |
| title_short |
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_sort |
n=4 multi-particle mechanics, wdvv equation and roots |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146796 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:25:50Z |
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