The Quantum Hall Effect on R^4

Abstract

Zhang and Hu have formulated an SU(2) quantum Hall system on the four-sphere, with interesting three-dimensional boundary dynamics including gapless states of nonzero helicity. In order to understand the local physics of their model we study the U(1) and SU(2) quantum Hall systems on flat R^4, with flat boundary R^3. In the U(1) case the boundary dynamics is essentially one dimensional. The SU(2) theory can be formulated on R^4 for any isospin I, but in order to obtain a flat boundary theory we must take I \to \infty as in Zhang and Hu. The theory simplifies in the limit, the boundary becoming a collection of one-dimensional systems. We also discuss general constraints on the emergence of gravity from nongravitational field theories.

24 pages

References in corpus (4)

• A Four Dimensional Generalization of the Quantum Hall Effect
• Anti De Sitter Space And Holography
• Quantum Hall Effect in Higher Dimensions
• Collective excitations at the boundary of a 4D quantum Hall droplet

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• Challenges for Emergent Gravity
• A primordial theory
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Rigid open membrane and non-abelian non-commutative Chern-Simons theory