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 \( {\partial}_m^4F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. \) 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 \( {\partial}_{\tau }{\partial}_{\overline{\tau}}{\partial}_m^2F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. \), 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.

当SU（N）\（\ mathcal {N} \） = 4时，具有复杂轨距耦合τ的超阳密斯（SYM）理论被放置在一个圆形的四个球体上，并通过\（\ mathcal {N} \） = 2保留质量参数m，可以使用超对称定位精确计算其自由能F（m，τ， \（\ overline {\ tau} \））。在这项工作中，我们得出了四阶导数\（{\ partial} _m ^ 4F \ left（m，\ tau，\ overline {\ tau} \ right）\ left | {{} _ m} _ { = 0} \ right。\）\（\ mathcal {N} \）中的球体自由能和集成的应力张量多重四点函数= 4 SYM理论。然后，我们将这种精确的关系以及先前工作中得出的各种其他约束条件（来自解析引导程序，混合导数\（{\ partial} _ {\ tau} {\ partial} _ {\ overline {\ tau}} { \ partial} _m ^ 2F \ left（m，\ tau，\ overline {\ tau} \ right）\ left | {{} _ m} _ {= 0} \ right。\），以及类型IIB超弦理论的散射幅度）确定在分离点上\（\ mathcal {N} \） = 4 SYM相关器的大N和大't Hooft耦合λ展开中的各种摄动项。特别是，我们确定\（\ mathcal {N} \） = 4 SYM相关函数中的前导大λ项，其阶数为1 / N ⁸。这超出了平面极限三个数量级。