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