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added a graphics (here) illustrating how what one might call the “shape observables” on the fuzzy 2-sphere (the integrals “$\int_{S^2_N} (R^{2k})$” for any choice of fixing the ordering ambiguity of the integrand) are encoded by chord diagrams, and are in fact $\mathfrak{sl}(2)$-weight system Vassiliev invariants.
To give this a little bit of a home, I added a minimum of text around that, and in order to give that text a bit of a home I added some further text with basics on the definition of the fuzzy 2-sphere.
am adding pointers on the fuzzy 3-sphere:
The fuzzy 3-sphere was first discussed (in the context of D0-brane-systems) in
Discussion in the context of M2-M5-brane bound states/E-strings:
added the original references on the fuzzy 4-sphere:
Harald Grosse, Ctirad Klimcik, P. Presnajder, On Finite 4D Quantum Field Theory in Non-Commutative Geometry, Commun. Math. Phys.180:429-438, 1996 (arXiv:hep-th/9602115)
Judith Castelino, Sangmin Lee, Washington Taylor, Longitudinal 5-branes as 4-spheres in Matrix theory, Nucl. Phys. B526:334-350, 1998 (arXiv:hep-th/9712105)
(via D5-branes)
added references on the fuzzy 6-sphere and higher:
Sanjaye Ramgoolam, Section 5 of: On spherical harmonics for fuzzy spheres in diverse dimensions, Nucl. Phys. B610: 461-488, 2001 (arXiv:hep-th/0105006)
Yusuke Kimura, On Higher Dimensional Fuzzy Spherical Branes, Nucl. Phys. B664 (2003) 512-530 (arXiv:hep-th/0301055)
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