Peer-Reviewed Journal Details
Mandatory Fields
Dolan B.;Nash C.
Journal of High Energy Physics
Chiral fermions and Spinc structures on matrix approximations to manifolds
Optional Fields
Field Theories in Higher Dimensions Gauge Symmetry M(atrix) Theories Standard Model
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 Spinc 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 ℂℙ2. The unitary grassmannian U(5)/ (U(3) ×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. © SISSA/ISAS 2002.
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