Nonplanar integrated correlator in N=4 SYM

The integrated correlator of four superconformal stress-tensor primaries in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mi>N</a:mi><a:mo stretchy="false">)</a:mo></a:math> <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="script">N</e:mi><e:mo>=</e:mo><e:mn>4</e:mn></e:math> super Yang-Mills (SYM) theory in the perturbative limit takes a remarkably simple form, where the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>L</h:mi></h:math>-loop coefficient is given by a rational multiple of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>ζ</j:mi><j:mo stretchy="false">(</j:mo><j:mn>2</j:mn><j:mi>L</j:mi><j:mo>+</j:mo><j:mn>1</j:mn><j:mo stretchy="false">)</j:mo></j:math>. In this paper, we extend the previous analysis of expressing the perturbative integrated correlator as a linear combination of periods of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>f</n:mi></n:math>-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 <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>f</p:mi></p:math>-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.