The standard prescription for calculating a Wilson loop in the AdS/CFT
correspondence is by a string world-sheet ending along the loop at the
boundary of AdS. For a multiply wrapped Wilson loop this leads to many
coincident strings, which may interact among themselves. In such cases
a better description of the system is in terms of a D3-brane carrying
electric flux. I describe such solutions for the single straight line
and the circular loop. The action agrees with the string calculation at
small coupling and in addition captures all the higher genus
corrections at leading order in alpha'. The resulting expression is in
remarkable agreement with that found from a zero dimensional Gaussian
matrix model.