Far beyond the planar limit in strongly-coupled mathcal{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^4Fleft(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^2Fleft(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.