Nonplanar integrated correlator in $N=4$ SYM

The integrated correlator of four superconformal stress-tensor primaries in $SU\left(N\right)$ $N=4$ super Yang-Mills (SYM) theory in the perturbative limit takes a remarkably simple form, where the $L$-loop coefficient is given by a rational multiple of $\zeta (2L+1)$. In this paper, we extend the previous analysis of expressing the perturbative integrated correlator as a linear combination of periods of $f$-graphs, graphical representations for loop integrands, to the nonplanar sector at four loops. At this loop order, multiple zeta values make their first appearance when evaluating periods of nonplanar $f$-graphs, but cancel nontrivially in the weighted sum. The remaining single zeta value, along with the rational number prefactor, makes a perfect agreement with the prediction from supersymmmetric localization.