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The Standard Model Fermion Spectrum From Complex Projective Spaces

Brian P. Dolan1,2 and C. Nash1,2

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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) × U(1) gauge fields. The construction may have applications in type-IIA string theory and non-commutative geometry.


Keywords

Differential and Algebraic Geometry

M(atrix) Theories

Non-Commutative Geometry

Field Theories in Higher Dimensions

PACS

11.15.-q Gauge field theories

14.60.Lm Ordinary neutrinos (nue, numu, nutau)

02.40.Gh Noncommutative geometry

11.25.Yb M theory

11.30.Ly Other internal and higher symmetries

11.10.Kk Field theories in dimensions other than four

Subjects

Mathematical physics

Particle physics and field theory

Dates

Issue 10 (October 2002)

Received 15 July 2002, accepted for publication 16 October 2002

Published 4 November 2002



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