On spherical harmonics for fuzzy spheres in diverse dimensions |
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Authors: | Sanjaye Ramgoolam |
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Institution: | Department of Physics, Brown University, Providence, RI 02912, USA |
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Abstract: | 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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