A tale of superfluids, two-dimensional electromagnetism and the quantum hall effect

Can Maxwell’s electromagnetism emerge in a two dimensional quantum mechanical system?  This appears to be ruled out in lattice gauge theories by an instability towards confinement that forbids quasi-free charges at low energies, in analogy with quark confinement in quantum chromodynamics.  However, using the boson-vortex duality, I will illustrate how conventional superfluids are indeed a quantum mechanical realization of Maxwell’s electromagnetism, with charges corresponding to superfluid vortices and the photon to the superfluid sound mode.  Then I will describe a recent extension of this mapping involving Maxwell’s theory coupled to a Dirac fermion, and how these ideas have offered us a new window into one of the few fractionalized metals known to occur in nature: the composite fermion sea in the quantum Hall regime. I will close by describing how this mapping allowed us to uncover a hidden connection between this state and another celebrated quantum Hall phase: the bilayer exciton condensate.