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

A bstract When the SU( N ) 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 N = 2-preserving mass parameter m , its free energy F ( m, τ, τ̄ τ ¯ ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative ∂ₘ⁴F(m,τ, τ̄)|ₘ₌₀. ∂ m 4 F m τ τ ¯ m = 0 of the sphere free energy and the integrated stress-tensor multiplet four-point function in the N 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∂τ̄∂ₘ²F(m,τ, τ̄)|ₘ₌₀. ∂ τ ∂ τ ¯ ∂ m 2 F m τ τ ¯ 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 N = 4 SYM correlator at separated points. In particular, we determine the leading large- λ term in the N N = 4 SYM correlation function at order 1 /N 8 . This is three orders beyond the planar limit.