DUAL RESPONSE MODELS FOR THE FRACTIONAL QUANTUM HALL-EFFECT

It is shown that the Jain mapping between integer and fractional quant um Hall systems can be described as a dynamical renormalization of an effective Chern-Simons field theory. The effects of mirror symmetry of compactified string theory on this system are studied and it is shown that, when the gauge group is compact, the mirror map has the same ef fect as the Sain map. The ingredients of the Jain construction appear as topologically nontrivial field configurations, of the compact gauge theory giving a dynamical origin for the Jain hierarchy. [S0163-1829( 98)02536-3].