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Monopoles, affine algebras and the gluino condensate

Valentin V. Khoze, N. Michael Davies, Timothy Hollowood Orcid Logo

Journal of Mathematical Physics, Volume: "44", Issue: 8, Pages: 3640 - 3656

Swansea University Author: Timothy Hollowood Orcid Logo

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DOI (Published version): 10.1063/1.1586477

Abstract

We examine the low-energy dynamics of four-dimensional supersymmetric gauge theories and calculate the values of the gluino condensate for all simple gauge groups. By initially compactifying the theory on a cylinder we are able to perform calculations in a controlled weakly-coupled way for small rad...

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Published in: Journal of Mathematical Physics
ISSN: 00222488
Published: 2000
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URI: https://cronfa.swan.ac.uk/Record/cronfa28551
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spelling 2016-06-03T14:36:32.6221691 v2 28551 2016-06-03 Monopoles, affine algebras and the gluino condensate ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 2016-06-03 SPH We examine the low-energy dynamics of four-dimensional supersymmetric gauge theories and calculate the values of the gluino condensate for all simple gauge groups. By initially compactifying the theory on a cylinder we are able to perform calculations in a controlled weakly-coupled way for small radius. The dominant contributions to the path integral on the cylinder arise from magnetic monopoles which play the role of instanton constituents. We find that the semi-classically generated superpotential of the theory is the affine Toda potential for an associated twisted affine algebra. We determine the supersymmetric vacua and calculate the values of the gluino condensate. The number of supersymmetric vacua is equal to c_2, the dual Coxeter number, and in each vacuum the monopoles carry a fraction 1/c_2 of topological charge. As the results are independent of the radius of the circle, they are also valid in the strong coupling regime where the theory becomes decompactified. In this way we obtain values for the gluino condensate which for the classical gauge groups agree with previously known ``weak coupling instanton'' expressions (but not with the ``strong coupling instanton'' calculations). This detailed agreement provides further evidence in favour of the recently advocated resolution of the the gluino condensate puzzle. We also make explicit predictions for the gluino condensate for the exceptional Journal Article Journal of Mathematical Physics "44" 8 3640 3656 00222488 30 6 2000 2000-06-30 10.1063/1.1586477 http://inspirehep.net/record/528105 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2016-06-03T14:36:32.6221691 2016-06-03T14:36:32.3725675 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Valentin V. Khoze 1 N. Michael Davies 2 Timothy Hollowood 0000-0002-3258-320X 3
title Monopoles, affine algebras and the gluino condensate
spellingShingle Monopoles, affine algebras and the gluino condensate
Timothy Hollowood
title_short Monopoles, affine algebras and the gluino condensate
title_full Monopoles, affine algebras and the gluino condensate
title_fullStr Monopoles, affine algebras and the gluino condensate
title_full_unstemmed Monopoles, affine algebras and the gluino condensate
title_sort Monopoles, affine algebras and the gluino condensate
author_id_str_mv ea9ca59fc948276ff2ab547e91bdf0c2
author_id_fullname_str_mv ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy Hollowood
author Timothy Hollowood
author2 Valentin V. Khoze
N. Michael Davies
Timothy Hollowood
format Journal article
container_title Journal of Mathematical Physics
container_volume "44"
container_issue 8
container_start_page 3640
publishDate 2000
institution Swansea University
issn 00222488
doi_str_mv 10.1063/1.1586477
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/528105
document_store_str 0
active_str 0
description We examine the low-energy dynamics of four-dimensional supersymmetric gauge theories and calculate the values of the gluino condensate for all simple gauge groups. By initially compactifying the theory on a cylinder we are able to perform calculations in a controlled weakly-coupled way for small radius. The dominant contributions to the path integral on the cylinder arise from magnetic monopoles which play the role of instanton constituents. We find that the semi-classically generated superpotential of the theory is the affine Toda potential for an associated twisted affine algebra. We determine the supersymmetric vacua and calculate the values of the gluino condensate. The number of supersymmetric vacua is equal to c_2, the dual Coxeter number, and in each vacuum the monopoles carry a fraction 1/c_2 of topological charge. As the results are independent of the radius of the circle, they are also valid in the strong coupling regime where the theory becomes decompactified. In this way we obtain values for the gluino condensate which for the classical gauge groups agree with previously known ``weak coupling instanton'' expressions (but not with the ``strong coupling instanton'' calculations). This detailed agreement provides further evidence in favour of the recently advocated resolution of the the gluino condensate puzzle. We also make explicit predictions for the gluino condensate for the exceptional
published_date 2000-06-30T03:34:46Z
_version_ 1763751479015899136
score 11.036706

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