Fuzzy Complex Quadrics and Spheres

Abstract

A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These matrix algebras contain the relevant degrees of freedom for describing truncations of harmonic expansions of functions on N-spheres. An Inonu-Wigner contraction of the quadric gives the co-tangent bundle to the commutative sphere in the continuum limit. It is shown how the degrees of freedom for the sphere can be projected out of a finite dimensional functional integral, using second-order Casimirs, giving a well-defined procedure for construction functional integrals over fuzzy spheres of any dimension.

11 pages,typeset in LaTeX, uses yougtab.sty

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Cited by in corpus (20)

• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• A Gauge-Invariant UV-IR Mixing and The Corresponding Phase Transition For U(1) Fields on the Fuzzy Sphere
• Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere
• Resolving brane collapse with 1/N corrections in non-Abelian DBI
• Fuzzy Toric Geometries
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• Construction of fuzzy S^4
• Nonabelian gauge field and dual description of fuzzy sphere
• Finite N effects on the collapse of fuzzy spheres
• Quantum Black Holes: the Event Horizon as a Fuzzy Sphere
• The One-Plaquette Model Limit of NC Gauge Theory in 2D
• Fuzzy circle and new fuzzy sphere through confining potentials and energy cutoffs
• Heat kernel coefficients for compact fuzzy spaces
• Off-shell nilpotent (anti-)BRST symmetries for a free particle system on a toric geometry: superfield formalism
• Noncommutative Spherically Symmetric Spaces
• Fuzzy hyperspheres via confining potentials and energy cutoffs
• A projective Dirac operator on CP^2 within fuzzy geometry
• The $x_i$-eigenvalue problem on some new fuzzy spheres
• Fuzzy Torus via q-Parafermion
• General $O(D)$-equivariant fuzzy hyperspheres via confining potentials and energy cutoffs