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Chiral Fermions and Spinc structures on Matrix approximations to manifolds

Brian P. Dolan·C. Nash
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Abstract

The Atiyah-Singer index theorem is investigated on various compact manifolds which admit finite matrix approximations (``fuzzy spaces'') with a view to applications in a modified Kaluza-Klein type approach in which the internal space consists of a finite number of points. Motivated by the chiral nature of the standard model spectrum we investigate manifolds that do not admit spinors but do admit $Spin^c$ structures. It is shown that, by twisting with appropriate bundles, one generation of the electroweak sector of the standard model, including a right-handed neutrino, can be obtained in this way from the complex projective space $\CP^2$. The unitary Grassmannian $U(5)/(U(3)\times U(2))$ yields a spectrum that contains the correct charges for the Fermions of the standard model, with varying multiplicities for the different particle states.

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Brian P. Dolan, C. Nash. 2002-09-24. Chiral Fermions and Spinc structures on Matrix approximations to manifolds. https://doi.org/10.1088/1126-6708%2F2002%2F07%2F057

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