Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions

Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This remarkable property, based on the reduction of couplings at the...

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Дата:2008
Автори: Mondragón, M., Zoupanos, G.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2008
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/148978
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions / M. Mondragón, G. Zoupanos // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 88 назв. — англ.

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spelling irk-123456789-1489782019-02-21T01:23:42Z Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions Mondragón, M. Zoupanos, G. Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduction in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the supersymmetric spectrum in the dimensionful sector. Here we examine the predictions of two such FUTs. Next we consider gauge theories defined in higher dimensions, where the extra dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a generalized à la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging such as (i) the appearance of non-Abelian gauge theories in four dimensions starting from an Abelian gauge theory in higher dimensions, (ii) the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii) the renormalizability of the theory both in higher as well as in four dimensions. Then reversing the above approach we present a renormalizable four dimensional SU(N) gauge theory with a suitable multiplet of scalar fields, which via spontaneous symmetry breaking dynamically develops extra dimensions in the form of a fuzzy sphere SN². We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M⁴ × S², the scalars being interpreted as gauge fields on S². Depending on the parameters of the model the low-energy gauge group can be SU(n), or broken further to SU(n₁) × SU(n₂) × U(1). Therefore the second picture justifies the first one in a renormalizable framework but in addition has the potential to reveal new aspects of the theory. 2008 Article Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions / M. Mondragón, G. Zoupanos // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 88 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81T60; 81V22; 83E15; 81T75; 54A40 http://dspace.nbuv.gov.ua/handle/123456789/148978 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduction in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the supersymmetric spectrum in the dimensionful sector. Here we examine the predictions of two such FUTs. Next we consider gauge theories defined in higher dimensions, where the extra dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a generalized à la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging such as (i) the appearance of non-Abelian gauge theories in four dimensions starting from an Abelian gauge theory in higher dimensions, (ii) the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii) the renormalizability of the theory both in higher as well as in four dimensions. Then reversing the above approach we present a renormalizable four dimensional SU(N) gauge theory with a suitable multiplet of scalar fields, which via spontaneous symmetry breaking dynamically develops extra dimensions in the form of a fuzzy sphere SN². We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M⁴ × S², the scalars being interpreted as gauge fields on S². Depending on the parameters of the model the low-energy gauge group can be SU(n), or broken further to SU(n₁) × SU(n₂) × U(1). Therefore the second picture justifies the first one in a renormalizable framework but in addition has the potential to reveal new aspects of the theory.
format Article
author Mondragón, M.
Zoupanos, G.
spellingShingle Mondragón, M.
Zoupanos, G.
Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Mondragón, M.
Zoupanos, G.
author_sort Mondragón, M.
title Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
title_short Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
title_full Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
title_fullStr Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
title_full_unstemmed Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
title_sort unified gauge theories and reduction of couplings: from finiteness to fuzzy extra dimensions
publisher Інститут математики НАН України
publishDate 2008
url http://dspace.nbuv.gov.ua/handle/123456789/148978
citation_txt Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions / M. Mondragón, G. Zoupanos // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 88 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT mondragonm unifiedgaugetheoriesandreductionofcouplingsfromfinitenesstofuzzyextradimensions
AT zoupanosg unifiedgaugetheoriesandreductionofcouplingsfromfinitenesstofuzzyextradimensions
first_indexed 2023-05-20T17:31:56Z
last_indexed 2023-05-20T17:31:56Z
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