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

Abstract

We show how the elliptic Calogero-Moser integrable systems arise from a symplectic quotient construction, generalising the construction for A_{N-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 construction 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 associated 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.

22 pages, uses latex; v2: references added

References in corpus (5)

• A Large N Duality via a Geometric Transition
• Orientifold planes, affine algebras and magnetic monopoles
• An Exact Elliptic Superpotential for N=1^* Deformations of Finite N=2 Gauge Theories
• Vacuum states of N=1* mass deformations of N=4 and N=2 conformal gauge theories and their brane interpretations
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Cited by in corpus (11)

• Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models
• N=1* vacua, Fuzzy Spheres and Integrable Systems
• The N=1* Theories on R^{1+2} X S^1 with Twisted Boundary Conditions
• Counting the Massive Vacua of N=1* Super Yang-Mills Theory
• Conformal S-dualities from O-planes
• A note on S-duality for the N=1* Sp(2n) and SO(2n+1) super-Yang-Mills theories
• Duality and Modularity in Elliptic Integrable Systems and Vacua of N=1* Gauge Theories
• On the N=1* Gauge Theory on a Circle and Elliptic Integrable Systems
• Permutations of Massive Vacua
• Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems and KZB equations
• Global variants of $\mathcal{N}=1^{\ast }$ theories and Calogero-Moser systems