On spherical harmonics for fuzzy spheres in diverse dimensions

By Sanjaye Ramgoolam. 2001

170 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5d0d4b3834868cfb5cb3fedb5aa0bc888ac6926c

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Citations in the corpus

Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance (2001, background): “I am optimistic that the main theorem of the present paper can in some form be extended (by different methods) to more general homogeneous spaces, such as higher-dimensional spheres [42], since one still has available the action of a compact Lie group which is so heavily used here.”
n-ary algebras: a review with applications (2010, background): “[308]; see also [309] in the context of fuzzy spheres).”
Selfdual strings and loop space Nahm equations (2008, methodology): “The construction of the fuzzy three-sphere [2] is complicated compared to the fuzzy two-sphere.”
Tiny graviton matrix theory: DLCQ of IIB plane-wave string theory, a conjecture (2004, background): “To construct a fuzzy three sphere of generic radius, we start with matrices made out of a sequence of n Γ’s and 4× 4 identity matrices [32, 33] : L ≡ (Γ ⊗ 1⊗ 1⊗ · · · ⊗ 1 + 1⊗ Γ ⊗ · · · ⊗ 1 + · · ·+ 1⊗ 1⊗ · · · ⊗ Γ)sym , (D.”