  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. We
find 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.
