paper

Unified Theories from Fuzzy Extra Dimensions

arXiv:hep-th/0401200 · doi:10.1002/prop.200410168

Abstract

We combine and exploit ideas from Coset Space Dimensional Reduction (CSDR) methods and Non-commutative Geometry. We consider the dimensional reduction of gauge theories defined in high dimensions where the compact directions are a fuzzy space (matrix manifold). In the CSDR one assumes that the form of space-time is M^D=M^4 x S/R with S/R a homogeneous space. Then a gauge theory with gauge group G defined on M^D can be dimensionally reduced to M^4 in an elegant way using the symmetries of S/R, in particular the resulting four dimensional gauge is a subgroup of G. In the present work we show that one can apply the CSDR ideas in the case where the compact part of the space-time is a finite approximation of the homogeneous space S/R, i.e. a fuzzy coset. In particular we study the fuzzy sphere case.

6 pages, Invited talk given by G. Zoupanos at the 36th International Symposium Ahrenshoop, Wernsdorf, Germany, 26-30 Aug 2003

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