Discrete Kaluza-Klein from scalar fluctuations in noncommutative geometry
arXiv:hep-th/0104108 · doi:10.1063/1.1418012
Abstract
We compute the metric associated to noncommutative spaces described by a tensor product of spectral triples. Well known results of the two-sheets model (distance on a sheet, distance between the sheets) are extended to any product of two spectral triples. The distance between different points on different fibres is investigated. When one of the triple describes a manifold, one find a Pythagorean theorem as soon as the direct sum of the internal states (viewed as projections) commutes with the internal Dirac operator. Scalar fluctuations yield a discrete Kaluza-Klein model in which the extra metric component is given by the internal part of the geometry. In the standard model, this extra component comes from the Higgs field.
References added. Argument in example of commutative spaces precised. Proposition 3 (very) slightly generalised
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