The Quantum Hall Effect on R

Zhang and Hu have formulated an SU(2) quantum Hall system on the foursphere, 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 R4, with flat boundary R3. In the U(1) case the boundary dynamics is essentially one dimensional. The SU(2) theory can be formulated on R4 for any isospin I, but in order to obtain a flat boundary theory we must take I → ∞ 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.