Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

Abstract

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.

arXiv comment34 pages, v2 contains minor corrections to the published version

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• Evidence for F(uzz) Theory
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• Fuzzy Toric Geometries
• Spin $j$ Dirac Operators on the Fuzzy 2-Sphere
• Areas and entropies in BFSS/gravity duality
• Large N reduction on coset spaces
• Triple Point of a Scalar Field Theory on a Fuzzy Sphere
• Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $C{P}^3$ as a $S_F^2$ bundle over $S_F^4$
• Vector bundles for "Matrix algebras converge to the sphere"
• The matrix regularization for Riemann surfaces with magnetic fluxes
• Dirac operators for matrix algebras converging to coadjoint orbits
• Laplacians on Fuzzy Riemann Surfaces
• Noncommutative Spherically Symmetric Spaces
• Monopoles On $S_F^2$ From The Fuzzy Conifold
• The fuzzy BTZ
• A projective Dirac operator on CP^2 within fuzzy geometry
• Unusual Thermodynamics on the Fuzzy 2-Sphere