Holographic correspondence between electrodynamics in three and four dimensions

We show that correlators of the gauge field in 3D electrodynamics with N flavors of massless matter can be obtained, in the leading order of the large N expansion, from solutions of free classical electrodynamics in a 4D half-space for which the 3D space is the boundary. The Abelian gauge fields of the two theories are dual to each other. We conjecture that for 3D scalar electrodynamics this duality still holds in the infrared when the 4D theory is moved into the Higgs phase. We use this conjecture to argue that condensation of monopoles (as opposed to a dilute gas of them) drives the large N 3D scalar electrodynamics away from criticality and into confinement. Typeset using REVTEX