Eight-dimensional quantum Hall effect and "octonions"
TLDR
A generalization of the quantum Hall effect where particles move in an eight-dimensional space under an SO(8) gauge field is constructed, where two fundamentally different liquids with distinct configuration spaces can be constructed, depending on whether the particles carry spinor or vector SO( 8) quantum numbers.Abstract:
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 configuration 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 with an internal component of SO(7) holonomy, whereas the second liquid lives on a 14-dimensional manifold with an internal component of G2 holonomy.read more
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Journal ArticleDOI
Octonionic Electrodynamics
TL;DR: In this paper, Dirac's operator and Maxwell's equations in vacuum were derived in the algebra of split octonions and approximations were given which lead to classical Maxwell-Heaviside equations from full octonionic equations.
Journal ArticleDOI
Generalized Octonion Electrodynamics
TL;DR: In this article, the generalized field equation of dyons was reformulated in terms of octonion variables, and the generalized potential and current equations were discussed in a consistent manner, and it has been shown that due to the non associativity of OCTI variables it is necessary to impose certain constraints to describe generalized OCTI electrodynamics in a manifestly covariant and consistent manner.
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Open heterotic strings
TL;DR: In this paper, the authors classify potential cosmic strings according to the topological charge measurable outside the string core, and they conjecture that in string theory it is this charge that governs the stability of long strings.
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Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry
Dimitra Karabali,V. P. Nair +1 more
TL;DR: In this paper, a review of the quantum Hall effect in higher dimensions and its relation to fuzzy spaces is given, and the possible relevance of these ideas to fuzzy gravity is explained.
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Octonionic Version of Dirac Equations
TL;DR: In this paper, it was shown that a simple continuity condition in the algebra of split octonions suffices to formulate a system of differential equations that are equivalent to the standard Dirac equations.