The Standard Model Fermion Spectrum From Complex Projective spaces

Abstract

It is shown that the quarks and leptons of the standard model, including a right-handed neutrino, can be obtained by gauging the holonomy groups of complex projective spaces of complex dimensions two and three. The spectrum emerges as chiral zero modes of the Dirac operator coupled to gauge fields and the demonstration involves an index theorem analysis on a general complex projective space in the presence of topologically non-trivial SU(n)xU(1) gauge fields. The construction may have applications in type IIA string theory and non-commutative geometry.

13 pages. Typset using LaTeX and JHEP3 style files. Minor typos corrected

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Cited by in corpus (10)

• Finite Gauge Theory on Fuzzy CP^2
• Fermions on spontaneously generated spherical extra dimensions
• Extended Supersymmetries and the Dirac Operator
• On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
• A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking
• Dimensional Reduction and Vacuum Structure of Quiver Gauge Theory
• A projective Dirac operator on CP^2 within fuzzy geometry
• A projective Dirac operator on $\mathbb{C}{P}^n$ and extended SUSY