Dimensional Reduction over Fuzzy Coset Spaces

TL;DR

This paper explores gauge theories on Minkowski space-time extended with fuzzy coset spaces, providing a framework for dimensional reduction from non-commutative finite matrix approximations of extra dimensions.

Contribution

It establishes the rules for dimensional reduction of gauge theories on fuzzy coset spaces, including fermion fields, from higher dimensions to four-dimensional effective theories.

Findings

Reduction rules for gauge theories on fuzzy spaces derived

Fermion field dimensional reduction analyzed

Framework applicable to non-commutative extra dimensions

Abstract

We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined on this non-commutative setup is reduced to four dimensions and the rules of the corresponding dimensional reduction are established. We investigate in particular the case of the fuzzy sphere including the dimensional reduction of fermion fields.