The Eight Dimensional Quantum Hall Effect and the Octonions

Details The Eight Dimensional Quantum Hall Effect and the Octonions The Eight Dimensional Quantum Hall Effect and the Octonions

2003-06-02

arxiv.org/abs/cond-mat/0306045v1

Phys.Rev.Lett. 91 (2003) 236803

Physics

Condensed Matter

5 pages

Scientific paper

10.1103/PhysRevLett.91.236803

We construct a generalization of the quantum Hall effect where particles move in an eight dimensional space under an SO(8) gauge field. The underlying mathematics of this particle liquid is that of the last normed division algebra, the octonions. Two fundamentally different liquids with distinct configurations spaces can be constructed, depending on whether the particles carry spinor or vector SO(8) quantum numbers. One of the liquids lives on a 20 dimensional manifold of with an internal component of SO(7) holonomy, whereas the second liquid lives on a 14 dimensional manifold with an internal component of $G_2$ holonomy.

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