Novel Representation of an Integrated Correlator in N=4 Supersymmetric Yang-Mills Theory.

An integrated correlator of four superconformal stress-tensor primaries of N=4 supersymmetric SU(N) Yang-Mills theory (SYM), originally obtained by localization, is reexpressed as a two-dimensional lattice sum that is manifestly invariant under SL(2,Z) S duality. This expression is shown to satisfy a novel Laplace equation in the complex coupling constant τ that relates the SU(N) integrated correlator to those of the SU(N+1) and SU(N-1) theories. The lattice sum is shown to precisely reproduce known perturbative and nonperturbative properties of N=4 SYM for any finite N, as well as extending previously conjectured properties of the large-N expansion.