Unified theories from fuzzy extra dimensions

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 MD = M4 × S / R with S / R a homogeneous space. Then a gauge theory with gauge group G defined on MD can be dimensionally reduced to M4 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.