Abstract
We review recent work on a bosonic formulation of both anyon superconductivity and the fractional quantum Hall effect (FQHE). Central to this approach is the concept of charge-vortex duality in two-dimensional (2d) boson systems. A formal duality transformation which takes one from a particle to a vortex representation of a 2d boson model is described in detail. The duality transformation is employed to obtain detailed properties of both the FQHE hierarchy and a hierarchy of anyon superconducting phases.
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