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We investigate the origins and implications of the duality betweentopological insulators and topological superconductors in three and fourspacetime dimensions. In the latter, the duality transformation can be made atthe level of the path integral in the standard way, while in three dimensions,it takes the form of "self-duality in odd dimensions". In this sense, it isclosely related to the particle-vortex duality of planar systems. Inparticular, we use this to elaborate on Son's conjecture that a threedimensional Dirac fermion that can be thought of as the surface mode of a fourdimensional topological insulator is dual to a composite fermion.

Particle-vortex duality in topological insulators and superconductors