Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry

Details Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry

2006-06-17

arxiv.org/abs/hep-th/0606161v1

J.Phys.A39:12735-12764,2006

Physics

High Energy Physics

High Energy Physics - Theory

Invited review for Journal of Physics A; Mathematics and General, LaTeX, 43 pages

Scientific paper

10.1088/0305-4470/39/41/S05

We give a brief review of quantum Hall effect in higher dimensions and its relation to fuzzy spaces. For a quantum Hall system, the lowest Landau level dynamics is given by a one-dimensional matrix action whose large $N$ limit produces an effective action describing the gauge interactions of a higher dimensional quantum Hall droplet. The bulk action is a Chern-Simons type term whose anomaly is exactly cancelled by the boundary action given in terms of a chiral, gauged Wess-Zumino-Witten theory suitably generalized to higher dimensions. We argue that the gauge fields in the Chern-Simons action can be understood as parametrizing the different ways in which the large $N$ limit of the matrix theory is taken. The possible relevance of these ideas to fuzzy gravity is explained. Other applications are also briefly discussed.

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