SELF-DUALITY OF 3-DIMENSIONAL CHERN-SIMONS THEORY

We describe a precise self-duality relation between the electric charge and magnetic flux vortex sectors in the (2 + 1)-dimensional Z(N) gauge Higgs model with Chern-Simons term. The phase structure of this model is deduced using the self-duality. In particular, we find that the Chern-Simons term suppresses the confinement phase. Compact U(1) pure Chern-Simons theory corresponds to an N --> infinity, infinite bare gauge coupling and zero bare mass limit. The self-duality of Chern-Simons theory is used to explain the hierarchy of odd-denominator filling fractions in the fractional quantum Hall effect and to suggest similar hierarchical ground-state structures in theories of the anyon and high-temperature superconductivity. Possible extensions to the nonabelian gauge groups and connection to the two-dimensional conformal field theories are also discussed.