Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2010
• Автори: Chatzistavrakidis, A., Zoupanos, G.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2010
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/146306
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions / A. Chatzistavrakidis, Z. Zoupanos // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 87 назв. — англ.

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.