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

Abstract

When the SU(N) $\mathcal{N}$ = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an $\mathcal{N}$ = 2-preserving mass parameter m, its free energy F (m, τ,$\overline{\tau }$) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative ${\partial }_m^{4}F\left(m,\tau ,\overline{\tau }\right)\left|{{}_m}_{=0}\right)$ of the sphere free energy and the integrated stress-tensor multiplet four-point function in the $\mathcal{N}$ = 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 ${\partial }_{\tau }{\partial }_{\overline{\tau }}{\partial }_m^{2}F\left(m,\tau ,\overline{\tau }\right)\left|{{}_m}_{=0}\right)$, and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the $\mathcal{N}$ = 4 SYM correlator at separated points. In particular, we determine the leading large-λ term in the $\mathcal{N}$ = 4 SYM correlation function at order 1/N⁸. This is three orders beyond the planar limit.