Nonplanar integrated correlator in N=4 SYM

Abstract

The integrated correlator of four superconformal stress-tensor primaries in SU(N) 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 ζ(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. Published by the American Physical Society 2024