N=4 Multi-Particle Mechanics, WDVV Equation and Roots
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.
- Publication:
-
SIGMA
- Pub Date:
- March 2011
- DOI:
- 10.3842/SIGMA.2011.023
- arXiv:
- arXiv:1011.2207
- Bibcode:
- 2011SIGMA...7..023L
- Keywords:
-
- superconformal mechanics;
- Calogero models;
- WDVV equation;
- deformed root systems;
- High Energy Physics - Theory;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- SIGMA 7:023,2011