N=4 Multi-Particle Mechanics, WDVV Equation and Roots

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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dc.contributor.author	Lechtenfeld, O.
dc.contributor.author	Schwerdtfeger, K.
dc.contributor.author	Thürigen, J.
dc.date.accessioned	2019-02-11T15:22:02Z
dc.date.available	2019-02-11T15:22:02Z
dc.date.issued	2011
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 70E55; 81Q60; 17B22; 52B40; 05C65
dc.identifier.other	DOI:10.3842/SIGMA.2011.023
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/146796
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	N=4 Multi-Particle Mechanics, WDVV Equation and Roots	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA