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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
first_indexed 2013-09-26T11:46:08Z
last_indexed 2020-07-16T18:28:35Z
id cronfa16141
recordtype SURis
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spelling 2020-07-16T14:41:11.9953469 v2 16141 2013-09-20 Geometric construction of elliptic integrable systems and N=1* superpotentials 087fd097167d724ce1b13cb285741ef5 0000-0003-0867-4213 Prem Kumar Prem Kumar true false 2013-09-20 BGPS 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. Journal Article Journal of High Energy Physics 2002 01 020 020 31 12 2002 2002-12-31 10.1088/1126-6708/2002/01/020 COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University 2020-07-16T14:41:11.9953469 2013-09-20T11:13:20.6639083 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Prem Kumar 0000-0003-0867-4213 1 Jan Troost 2
title Geometric construction of elliptic integrable systems and N=1* superpotentials
spellingShingle Geometric construction of elliptic integrable systems and N=1* superpotentials
Prem Kumar
title_short Geometric construction of elliptic integrable systems and N=1* superpotentials
title_full Geometric construction of elliptic integrable systems and N=1* superpotentials
title_fullStr Geometric construction of elliptic integrable systems and N=1* superpotentials
title_full_unstemmed Geometric construction of elliptic integrable systems and N=1* superpotentials
title_sort Geometric construction of elliptic integrable systems and N=1* superpotentials
author_id_str_mv 087fd097167d724ce1b13cb285741ef5
author_id_fullname_str_mv 087fd097167d724ce1b13cb285741ef5_***_Prem Kumar
author Prem Kumar
author2 Prem Kumar
Jan Troost
format Journal article
container_title Journal of High Energy Physics
container_volume 2002
container_issue 01
container_start_page 020
publishDate 2002
institution Swansea University
doi_str_mv 10.1088/1126-6708/2002/01/020
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 0
active_str 0
description 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.
published_date 2002-12-31T06:30:06Z
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score 11.048171

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