Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-10-23
Annals Phys. 268 (1998) 61-104
Physics
High Energy Physics
High Energy Physics - Theory
40 pages LaTeX, 4 postscript files, uses psfig.sty; minor textual changes, typos corrected, references added
Scientific paper
10.1006/aphy.1998.5832
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 topological symmetries of Calabi-Yau sigma-models can be obtained from discrete geometric transformations of compact Chern-Simons gauge theory coupled to charged matter fields. We demonstrate that the appearence of magnetic monopole-instantons, which interpolate between topologically inequivalent vacua of the gauge theory, implies that the discrete symmetry 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 topologically non-trivial matter field and gauge degrees of freedom. We also apply the mirror transformation to the mean field theory of the quantum Hall effect. We show that it maps the Jain hierarchy into a new hierarchy of states in which the lowest composite fermions have the same filling fractions.
Cooper Larry
Kogan Ian I.
Szabo Richard J.
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