A Fuzzy Three Sphere and Fuzzy Tori

Abstract

A fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzy complex projective spaces, of complex dimension one and three, by modifying the Laplacians on the latter so as to give unwanted states large eigenvalues. This leaves only states corresponding to fuzzy spheres in the low energy spectrum (this allows the commutative algebra of functions on the continuous sphere to be approximated to any required degree of accuracy). The construction of a fuzzy circle opens the way to fuzzy tori of any dimension, thus circumventing the problem of power law corrections in possible numerical simulations on these spaces.

19 pages, typeset in LaTeX, uses youngtab.sty

References in corpus (5)

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• Higher dimensional geometries related to fuzzy odd-dimensional spheres
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• On Higher Dimensional Fuzzy Spherical Branes
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Cited by in corpus (20)

• The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories
• Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
• A matrix phase for the phi^4 scalar field on the fuzzy sphere
• Quantized Nambu-Poisson Manifolds and n-Lie Algebras
• Fuzzy Complex Quadrics and Spheres
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• Fuzzy Toric Geometries
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Construction of fuzzy S^4
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• Fuzzy circle and new fuzzy sphere through confining potentials and energy cutoffs
• Understanding truncated non-commutative geometries through computer simulations
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $C{P}^3$ as a $S_F^2$ bundle over $S_F^4$
• Quantum Hall Effect on Odd Spheres
• Fuzzy hyperspheres via confining potentials and energy cutoffs
• A projective Dirac operator on CP^2 within fuzzy geometry
• On localized and coherent states on some new fuzzy spheres
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry I: A QM/NCG Correspondence