Bulk Versus Edge in the Quantum Hall Effect
  The manifestation of the bulk quantum Hall effect on edge is the chiral anomaly. The chiral anomaly {\it is} the underlying principle of the ``edge approach'' of quantum Hall effect. In that approach, $\sxy$ should not be taken as the conductance derived from the space-local current-current correlation function of the pure one-dimensional edge problem. 
Y.-C. Kao and D.-H. Lee