The Standard Model Fermion Spectrum From Complex Projective spaces

TL;DR

This paper demonstrates how the fermion spectrum of the Standard Model, including right-handed neutrinos, can be derived from the geometry of complex projective spaces using index theorem analysis, with potential applications in string theory.

Contribution

It introduces a geometric construction of Standard Model fermions from complex projective spaces via index theorem and gauge field coupling, linking geometry to particle physics.

Findings

Fermion spectrum arises as chiral zero modes of the Dirac operator.

The construction includes right-handed neutrinos within the spectrum.

Potential applications in string theory and non-commutative geometry.

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.