MIRROR MAPS IN CHERN-SIMONS GAUGE-THEORY

We describe mirror symmetry in N = 2 superconformal field theories in terms of a dynamical topology changing process of the principal fiber bundle associated with a topological membrane. We show that the topolo gical symmetries of Calabi-Yau sigma-models can be obtained from discr ete geometric transformations of compact Chern-Simons gauge theory cou pled to charged matter fields. We demonstrate that the appearence of m agnetic monopole-instantons, which interpolate between topologically i nequivalent vacua of the gauge theory, implies that the discrete symme try group of the worldsheet theory is realized kinematically in three dimensions as the magnetic flux symmetry group. From this we construct the mirror map and show that it corresponds to the interchange of top ologically non-trivial matter field and gauge degrees of freedom. We a lso apply the mirror transformation to the mean field theory of the qu antum Hall effect. We show that it maps the Jain hierarchy into a new hierarchy of states in which the lowest composite fermions have the sa me filling fractions. (C) 1998 Academic Press.