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

Abstract

When the SU(N) N = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an N = 2-preserving mass parameter m, its free energy F (m, τ,τ¯) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative ∂m4F(mττ¯)|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 ∂τ∂τ¯∂m2F(mττ¯)|m=0, 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 N = 4 SYM correlator at separated points. In particular, we determine the leading large-λ term in the N = 4 SYM correlation function at order 1/N8. This is three orders beyond the planar limit.