Supersymmetric Chern-Simons theory and supersymmetric quantum Hall liquid

We develop a supersymmetric extension of Chern-Simons theory and Chern-Simons-Landau-Ginzburg theory for the supersymmetric quantum Hall liquid. Supersymmetric counterparts of topological and gauge structures peculiar to the Chern-Simons theory are inspected in the supersymmetric Chern-Simons theory. We also explore an effective field theoretical description for the supersymmetric quantum Hall liquid. The key observation is the charge-flux duality. Based on the duality, we derive a dual supersymmetric Chern-Simons-Landau-Ginzburg theory, and discuss physical properties of the topological excitations in the supersymmetric quantum Hall liquid.