Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators

Duality is a powerful theoretical tool whereby the strongly interacting and intractable regime of a theory can be accessed in terms of weakly interacting ``dual'' variables. In condensed matter, this is familiar from the Kramers-Wannier duality of the Ising model, and boson-vortex duality. Here, a duality for another fundamental problem -- Dirac fermions in two spatial dimensions -- is obtained, which provides a new window to the physics of strongly interacting electrons. This leads to unexpected connections between topological insulators in three dimensions and the physics of the half-filled Landau level, including composite fermions and Pfaffian quantum Hall states.