Doubleelliptic dynamical systems from generalized MukaiSklyanin algebras
Abstract
We consider the doubleelliptic generalisation of dynamical systems of CalogeroTodaRuijsenaars type using finitedimensional MukaiSklyanin algebras. The twobody system, which involves an elliptic dependence both on coordinates and momenta, is investigated in detail and the relation with Nambu dynamics is mentioned. We identify the 2D complex manifold associated with the double elliptic system as an elliptically fibered rational ("1/2K3") surface. Some generalisations are suggested which provide the ground for a description of the Nbody systems. Possible applications to SUSY gauge theories with adjoint matter in d=6 with two compact dimensions are discussed.
 Publication:

Nuclear Physics B
 Pub Date:
 July 2002
 DOI:
 10.1016/S05503213(02)002481
 arXiv:
 arXiv:hepth/0111066
 Bibcode:
 2002NuPhB.633..414B
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 31 pages, Latex