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Gauge Theories: From Kaluza–Klein to noncommutative gravity theories

1
Physics Department, National Technical University, GR-15780 Athens, Greece
2
Institute of Theoretical Physics, D-69120 Heidelberg, Germany
3
Max-Planck Institut für Physik, Fohringer Ring 6, D-80805 Munchen, Germany
4
Laboratoire d’ Annecy de Physique Theorique, 74940 Annecy, France
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 856; https://doi.org/10.3390/sym11070856
Received: 28 May 2019 / Revised: 18 June 2019 / Accepted: 20 June 2019 / Published: 2 July 2019
(This article belongs to the Special Issue Symmetry in Mathematical Cosmology)
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PDF [389 KB, uploaded 2 July 2019]

Abstract

First, the Coset Space Dimensional Reduction scheme and the best particle physics model so far resulting from it are reviewed. Then, a higher-dimensional theory in which the extra dimensions are fuzzy coset spaces is described and a dimensional reduction to four-dimensional theory is performed. Afterwards, another scheme including fuzzy extra dimensions is presented, but this time the starting theory is four-dimensional while the fuzzy extra dimensions are generated dynamically. The resulting theory and its particle content is discussed. Besides the particle physics models discussed above, gravity theories as gauge theories are reviewed and then, the whole methodology is modified in the case that the background spacetimes are noncommutative. For this reason, specific covariant fuzzy spaces are introduced and, eventually, the program is written for both the 3-d and 4-d cases. View Full-Text
Keywords: gauge theories; coset space dimensional reduction; fuzzy extra dimensions; higher-dimensional particle physics models; three-dimensional gravity; four-dimensional gravity; noncommutative spaces; fuzzy de Sitter gauge theories; coset space dimensional reduction; fuzzy extra dimensions; higher-dimensional particle physics models; three-dimensional gravity; four-dimensional gravity; noncommutative spaces; fuzzy de Sitter
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Manolakos, G.; Manousselis, P.; Zoupanos, G. Gauge Theories: From Kaluza–Klein to noncommutative gravity theories. Symmetry 2019, 11, 856.

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