A Curious Truncation ofN=4Supersymmetric Yang-Mills Theory

The coupling constant dependence of correlation functions of Bogomol'nyi-Prasad-Sommerfield operators in the $N=4$ supersymmetric Yang-Mills theory can be expressed in terms of integrated correlation functions. We approximate these integrated correlators by using a truncated operator product expansion. This leads to differential equations for the coupling dependence. When applied to a particular 16 point correlator, the coupling dependence we find agrees with the corresponding amplitude computed via the gauge theory/string theory correspondence. We conjecture that this truncation becomes exact in the large $N$ and large 't Hooft coupling limit.