Fuzzy spaces, the M(atrix) model and the quantum Hall effect

Abstract

This is a short review of recent work on fuzzy spaces in their relation to the M(atrix) theory and the quantum Hall effect. We give an introduction to fuzzy spaces and how the limit of large matrices is obtained. The complex projective spaces ${\mathbf{CP}}^k$, and to a lesser extent spheres, are considered. Quantum Hall effect and the behavior of edge excitations of a droplet of fermions on these spaces and their relation to fuzzy spaces are also discussed.

LaTeX, 33 pages, to appear in the Ian Kogan Memorial volume, ``From Fields to Strings: Circumnavigating Theoretical Physics'', ref.'s added

References in corpus (3)

• Construction of fuzzy S^4
• The Quantum Hall Effect on R^4
• Matrix models of 4-dimensional quantum Hall fluids

Cited by in corpus (24)

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• Quantum Hall Effect on the Flag Manifold F_2
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• Fuzzy circle and new fuzzy sphere through confining potentials and energy cutoffs
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• Quantum Hall Effect on the Grassmannians ${\mathbf{Gr}}_2({\mathbb{C}}^N)$
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• Noncommutative Deformations of Locally Symmetric Kähler manifolds