An exact prediction of N=4 supersymmetric Yang-Mills theory for string theory

We propose that the expectation value of a circular BPS-Wilson loop in N=4 supersymmetric Yang-Mills can be calculated exactly, to all orders in a 1/N expansion and to all orders in g(2)N. Using the AdS/CFT duality, this result yields a prediction of the value of the string amplitude with a circular boundary to all orders in alpha' and to all orders in g(s). We then compare this result with string theory. We find that the gauge theory calculation, for large g(2)N and to all orders in the 1/N-2 expansion, does agree with the leading string theory calculation, to all orders in g(s) and to lowest order in alpha'. We also find a relation between the expectation value of any closed smooth Wilson loop and the loop related to it by an inversion that takes a point along the loop to infinity, and compare this result, again successfully, with string theory. (C) 2001 American Institute of Physics.