Liouville Integrability of Classical Calogero-Moser Models

Liouville integrability of classical Calogero-Moser models is proved for models based on any root systems, including the non-crystallographic ones. It applies to all types of elliptic potentials, i.e. untwisted and twisted together with their degenerations (hyperbolic, trigonometric and rational), except for the rational potential models confined by a harmonic force.Comment: 8 pages, LaTeX2e, no figure

The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves

We study the elliptic C_n and BC_n Ruijsenaars-Schneider models which is elliptic generalization of system given in hep-th/0006004. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameterized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the systems corresponding to Calogero-Moser and Toda types.Comment: LaTeX2e, 25 pages, 1 table, some references added and rearranged together with misprints correcte

Geometric construction of elliptic integrable systems and N=1* superpotentials

We show how the elliptic Calogero-Moser integrable systems arise from a symplectic quotient construction, generalising the construction for AN −1 by Gorsky and Nekrasov to other algebras. This clarifies the role of (twisted) affine Kac-Moody algebras in elliptic Calogero-Moser systems and allows for a natural geometric con- struction of Lax operators for these systems. We elaborate on the connection of the associated Hamiltonians to superpotentials for N = 1∗ deformations of N = 4 supersymmetric gauge theory, and argue how non-perturbative physics generates the elliptic superpotentials. We also discuss the relevance of these systems and the asso- ciated quotient construction to open problems in string theory. In an appendix, we use the theory of orbit algebras to show the systematics behind the folding procedures for these integrable models