Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-05-01
Nucl.Phys. B610 (2001) 461-488
Physics
High Energy Physics
High Energy Physics - Theory
33 pages (Harvmac big), 1 figure v2: added footnote clarifying radius of fuzzy odd spheres, v3 : fixed minor typo in eq. 6.2
Scientific paper
10.1016/S0550-3213(01)00315-7
We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a natural basis which falls in correspondence with tensor constructions of irreducible representations of orthogonal groups SO(n). This basis is useful in describing fluctuations around various D-brane constructions of fuzzy spherical objects. The higher fuzzy spheres are non-associative algebras that appear as projections of associative algebras related to Matrices. The non-associativity (as well as the non-commutativity) disappears in the leading large $N$ limit, ensuring the correct classical limit. Some simple aspects of the combinatorics of the fuzzy four-sphere can be accounted by a heuristic picture of giant fractional instantons.
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