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The curve of compactified 6D gauge theories and integrable systems

Harry W. Braden, Timothy Hollowood Orcid Logo

Journal of High Energy Physics, Volume: "12", Issue: 12, Pages: 023 - 023

Swansea University Author: Timothy Hollowood Orcid Logo

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DOI (Published version): 10.1088/1126-6708/2003/12/023

Abstract

We analyze the Seiberg-Witten curve of the six-dimensional N=(1,1) gauge theory compactified on a torus to four dimensions. The effective theory in four dimensions is a deformation of the N=2* theory. The curve is naturally holomorphically embedding in a slanted four-torus--actually an abelian surfa...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: 2003
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URI: https://cronfa.swan.ac.uk/Record/cronfa28534
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first_indexed 2016-06-03T19:16:15Z
last_indexed 2018-02-09T05:12:46Z
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spelling 2016-06-03T14:36:19.5804855 v2 28534 2016-06-03 The curve of compactified 6D gauge theories and integrable systems ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 2016-06-03 SPH We analyze the Seiberg-Witten curve of the six-dimensional N=(1,1) gauge theory compactified on a torus to four dimensions. The effective theory in four dimensions is a deformation of the N=2* theory. The curve is naturally holomorphically embedding in a slanted four-torus--actually an abelian surface--a set-up that is natural in Witten's M-theory construction of N=2 theories. We then show that the curve can be interpreted as the spectral curve of an integrable system which generalizes the N-body elliptic Calogero-Moser and Ruijsenaars-Schneider systems in that both the positions and momenta take values in compact spaces. It turns out that the resulting system is not simply doubly elliptic, rather the positions and momenta, as two-vectors, take values in the ambient abelian surface. We analyze the two-body system in some detail. The system we uncover provides a concrete realization of a Beauville-Mukai system based on an abelian surface rather than a K3 Journal Article Journal of High Energy Physics "12" 12 023 023 1029-8479 30 11 2003 2003-11-30 10.1088/1126-6708/2003/12/023 http://inspirehep.net/record/632439 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2016-06-03T14:36:19.5804855 2016-06-03T14:36:19.3620841 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Harry W. Braden 1 Timothy Hollowood 0000-0002-3258-320X 2
title The curve of compactified 6D gauge theories and integrable systems
spellingShingle The curve of compactified 6D gauge theories and integrable systems
Timothy Hollowood
title_short The curve of compactified 6D gauge theories and integrable systems
title_full The curve of compactified 6D gauge theories and integrable systems
title_fullStr The curve of compactified 6D gauge theories and integrable systems
title_full_unstemmed The curve of compactified 6D gauge theories and integrable systems
title_sort The curve of compactified 6D gauge theories and integrable systems
author_id_str_mv ea9ca59fc948276ff2ab547e91bdf0c2
author_id_fullname_str_mv ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy Hollowood
author Timothy Hollowood
author2 Harry W. Braden
Timothy Hollowood
format Journal article
container_title Journal of High Energy Physics
container_volume "12"
container_issue 12
container_start_page 023
publishDate 2003
institution Swansea University
issn 1029-8479
doi_str_mv 10.1088/1126-6708/2003/12/023
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
url http://inspirehep.net/record/632439
document_store_str 0
active_str 0
description We analyze the Seiberg-Witten curve of the six-dimensional N=(1,1) gauge theory compactified on a torus to four dimensions. The effective theory in four dimensions is a deformation of the N=2* theory. The curve is naturally holomorphically embedding in a slanted four-torus--actually an abelian surface--a set-up that is natural in Witten's M-theory construction of N=2 theories. We then show that the curve can be interpreted as the spectral curve of an integrable system which generalizes the N-body elliptic Calogero-Moser and Ruijsenaars-Schneider systems in that both the positions and momenta take values in compact spaces. It turns out that the resulting system is not simply doubly elliptic, rather the positions and momenta, as two-vectors, take values in the ambient abelian surface. We analyze the two-body system in some detail. The system we uncover provides a concrete realization of a Beauville-Mukai system based on an abelian surface rather than a K3
published_date 2003-11-30T03:34:44Z
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score 11.036706

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