Details
| Original language | English |
|---|---|
| Article number | 023 |
| Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
| Volume | 7 |
| Publication status | Published - 2011 |
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.
Keywords
- Calogero models, Deformed root systems, Superconformal mechanics, WDVV equation
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Mathematical Physics
- Mathematics(all)
- Geometry and Topology
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In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 7, 023, 2011.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - N=4 multi-particle mechanics, WDVV equation and roots
AU - Lechtenfeld, Olaf
AU - Schwerdtfeger, Konrad
AU - Thürigen, Johannes
N1 - Copyright: Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
KW - Calogero models
KW - Deformed root systems
KW - Superconformal mechanics
KW - WDVV equation
UR - http://www.scopus.com/inward/record.url?scp=84255201982&partnerID=8YFLogxK
U2 - 10.3842/SIGMA.2011.023
DO - 10.3842/SIGMA.2011.023
M3 - Article
AN - SCOPUS:84255201982
VL - 7
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
SN - 1815-0659
M1 - 023
ER -