A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces

TL;DR

This paper constructs a universal Dirac operator for noncommutative spin bundles over fuzzy complex projective spaces, providing explicit spectra and eigenspinors, including new results for higher-dimensional cases.

Contribution

It introduces a universal Dirac operator and explicit noncommutative spin^c bundles over fuzzy CP^n, with novel spectral calculations for n≥3.

Findings

Explicit construction of noncommutative spin bundles

Calculation of Dirac spectra and eigenspinors

New spectral results for CP^n with n≥3

Abstract

We present a universal Dirac operator for noncommutative spin and spin^c bundles over fuzzy complex projective spaces. We give an explicit construction of these bundles, which are described in terms of finite dimensional matrices, calculate the spectrum and explicitly exhibit the Dirac eigenspinors. To our knowledge the spin^c spectrum for CP^n with n>=3 is new.