Wilson loops as D3-branes

We prove that the half-BPS Wilson loop operator of N = 4 SYM in a symmetric representation of the gauge group has a bulk gravitational description in terms of a single D3-brane in AdS(5) x S-5, as argued in hep-th/0604007. We also show that a half-BPS Wilson loop operator in an arbitrary representation is described by the D3-brane configuration proposed in hep-th/0604007. This is demonstrated by explicitly integrating out the degrees of freedom on the D3-branes and showing that they insert a half-BPS Wilson loop operator into the N = 4 SYM path integral in the desired representation.