Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 063, 47 pages      arXiv:1008.2049      http://dx.doi.org/10.3842/SIGMA.2010.063
Contribution to the Special Issue “Noncommutative Spaces and Fields”

Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions

Athanasios Chatzistavrakidis a, b and George Zoupanos b
a) Institute of Nuclear Physics, NCSR Demokritos, GR-15310 Athens, Greece
b) Physics Department, National Technical University of Athens, GR-15780 Zografou Campus, Athens, Greece

Received May 06, 2010, in final form July 22, 2010; Published online August 12, 2010

Abstract
Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle physics models in the context of higher-dimensional gauge theories with non-commutative extra dimensions. These ideas have been developed in two complementary ways, namely (i) starting with a higher-dimensional gauge theory and dimensionally reducing it to four dimensions over fuzzy internal spaces and (ii) starting with a four-dimensional, renormalizable gauge theory and dynamically generating fuzzy extra dimensions. We describe the above approaches and moreover we discuss the inclusion of fermions and the construction of realistic chiral theories in this context.

Key words: fuzzy extra dimensions; unified gauge theories; symmetry breaking.

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