On spherical harmonics for fuzzy spheres in diverse dimensions
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 con...
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| Published in | Nuclear physics. B Vol. 610; no. 3; pp. 461 - 488 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
10.09.2001
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| Online Access | Get full text |
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| Summary: | 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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| ISSN: | 0550-3213 1873-1562 |
| DOI: | 10.1016/S0550-3213(01)00315-7 |