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 z 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.

Automated summary

This study reexpresses the integrated correlator of four superconformal stress-tensor primaries of N = 4 supersymmetric SU(N) Yang-Mills theory as a two-dimensional lattice sum, which is shown to be invariant under SL (2, Z) S duality. The lattice sum is proven to satisfy a novel Laplace equation in the complex coupling constant z, connecting the SU(N) integrated correlator to those of the SU(N + 1) and SU(N - 1) theories. It accurately reproduces both perturbative and nonperturbative properties of N = 4 SYM for any finite N, as well as extending previously conjectured properties of the large-N expansion.