Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin Algebras

Details Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin Algebras Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin Algebras

2001-11-07

arxiv.org/abs/hep-th/0111066v1

Nucl.Phys. B633 (2002) 414-442

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, Latex

Scientific paper

10.1016/S0550-3213(02)00248-1

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 $d=6$ with two compact dimensions are discussed.

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