An exact prediction of NÄ4 supersymmetric Yang–Mills theory for string theory

We propose that the expectation value of a circular BPS-Wilson loop in N54 supersymmetric Yang–Mills can be calculated exactly, to all orders in a 1/N expansion and to all orders in gN . 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 a8 and to all orders in gs . We then compare this result with string theory. We find that the gauge theory calculation, for large gN and to all orders in the 1/N expansion, does agree with the leading string theory calculation, to all orders in gs and to lowest order in a8. 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. © 2001 American Institute of Physics. @DOI: 10.1063/1.1372177#