Far beyond the planar limit in strongly-coupled N=4 SYM

When the SU(N) N = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling tau is placed on a round four-sphere and deformed by an N = 2-preserving mass parameter m, its free energy F (m, tau,tau ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative partial derivative m4Fm tau tau m=0 of the sphere free energy and the integrated stress-tensor multiplet four-point function in the N = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative partial derivative tau partial derivative tau partial derivative m2Fm tau tau m=0, and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large 't Hooft coupling lambda expansion of the N = 4 SYM correlator at separated points. In particular, we determine the leading large-lambda term in the N = 4 SYM correlation function at order 1/N-8. This is three orders beyond the planar limit.

Automated summary

The study focuses on the N = 4 super-Yang-Mills theory placed on a round four-sphere and deformed by a mass parameter while using supersymmetric localization to compute the free energy. A new exact relation was derived between the fourth derivative of the sphere free energy and the stress-tensor multiplet four-point function in the N = 4 SYM theory, which was then utilized along with other constraints to determine various perturbative terms in the large N and large 't Hooft coupling lambda expansion. The leading large-lambda term in the N = 4 SYM correlation function at order 1/N-8 was determined, reaching three orders beyond the planar limit.