Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin Algebras
High Energy Physics - Theory
2009-11-07 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We consider the double-elliptic generalisation of dynamical systems of Calogero-Toda-Ruijsenaars type using finite-dimensional Mukai-Sklyanin algebras. The two-body 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 N-body systems. Possible applications to SUSY gauge theories with adjoint matter in with two compact dimensions are discussed.
Keywords
Cite
@article{arxiv.hep-th/0111066,
title = {Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin Algebras},
author = {H. Braden and A. Gorsky and A. Odesskii and V. Rubtsov},
journal= {arXiv preprint arXiv:hep-th/0111066},
year = {2009}
}
Comments
31 pages, Latex