Wilson loops in N=4 supersymmetric Yang-Mills theory

Perturbative computations of the expectation value of the Wilson loop in N = 4 supersymmetric Yang-Mills theory are reported. For the two special case s of a circular loop and a pair of antiparallel lines, it is shown that the sum of an infinite class of ladder-like planar diagrams, when extrapolated to strong coupling, produces an expectation value characteristic of the re sults of the AdS/CFT correspondence, (W) similar to exg((constant)root g(2) N). For the case of the circular loop, the sum is obtained analytically for all values of the coupling. In this case, the constant factor in front of root g(2)N also agrees with the supergravity results. We speculate that the sum of diagrams without internal vertices is exact for the circular loop a nd support this conjecture by showing that the leading corrections to the l adder diagrams cancel identically in four dimensions, We also show that, fo r arbitrary smooth loops, the ultraviolet divergences cancel to order g(4)N (2). (C) 2000 Elsevier Science B.V. All rights reserved.