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.