Wilson loops in N=4 supersymmetric Yang–Mills theory Original Research Article

Perturbative computations of the expectation value of the Wilson loop in N=4 supersymmetric Yang–Mills theory are reported. For the two special cases 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 results of the AdS/CFT correspondence, 〈W〉∼exp((constant)g2N). 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 g2N also agrees with the supergravity results. We speculate that the sum of diagrams without internal vertices is exact for the circular loop and support this conjecture by showing that the leading corrections to the ladder diagrams cancel identically in four dimensions. We also show that, for arbitrary smooth loops, the ultraviolet divergences cancel to order g4N2.