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

Prem Kumar Orcid Logo, Jan Troost

Journal of High Energy Physics, Volume: 2002, Issue: 01, Pages: 020 - 020

Swansea University Author: Prem Kumar Orcid Logo

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DOI (Published version): 10.1088/1126-6708/2002/01/020

Abstract

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...

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Published in: Journal of High Energy Physics
Published: 2002
URI: https://cronfa.swan.ac.uk/Record/cronfa16141
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Abstract: 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.
College: Faculty of Science and Engineering
Issue: 01
Start Page: 020
End Page: 020