Double-elliptic dynamical systems from generalized Mukai-Sklyanin algebras

H W Braden, A Gorsky, A Odesskii, V Rubtsov

Research output: Contribution to journalArticlepeer-review

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 d = 6 with two compact dimensions are discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)414-442
Number of pages29
JournalNuclear physics b
Volume633
Issue number3
Publication statusPublished - 1 Jul 2002

Keywords

  • RUIJSENAARS-SCHNEIDER MODEL
  • INTEGRABLE SYSTEMS
  • DUALITY
  • BUNDLES
  • K3

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