Dual Response Models for the Fractional Quantum Hall Effect

It is shown that the Jain mapping between states of integer and fractional quantum Hall systems can be described dynamically as a perturbative renormalization of an effective Chern-Simons field theory. The effects of mirror duality symmetries of toroidally 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 effect as the Jain map. The extrinsic ingredients of the Jain construction appear naturally as topologically non-trivial field configurations of the compact gauge theory giving a dynamical origin for the Jain hierarchy of fractional quantum Hall states.