Integrated Correlators in N=4 Supersymmetric Yang-Mills Theory beyond Localization.

We study integrated correlators of four superconformal primaries O_{p} with arbitrary charges p in N=4 super Yang-Mills theory. The ⟨O_{2}O_{2}O_{p}O_{p}⟩ integrated correlators can be computed by supersymmetric localization, whereas correlators with more general charges are currently not accessible from this method and, in general, contain complicated multiple zeta values. Nevertheless, we observe that, if one sums over the contributions from all different channels in a given correlator, then all the multiple zeta values (and products of ζ's) cancel, leaving only ζ(2ℓ+1) at ℓ loops. We then propose an exact expression of such integrated correlators in the planar limit, valid for arbitrary 't Hooft coupling. The expression matches with the known exact localization-based results for specific charges, as well as with all existing perturbative and strong-coupling results in the literature for more general charges. As an application, our result is used to determine certain seven-loop Feynman integral periods and fix previously unknown coefficients in the correlators at strong coupling.

Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N=4 Supersymmetric Yang-Mills Theory.

We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, conformal integrands grouped according to a hidden symmetry discovered for correlation functions. The answer we find exposes a fundamental tension between manifest locality and planarity with manifest conformality not seen at lower loops. For the first time, the integrand must include terms that are finite even on-shell and terms that are divergent even off-shell (so-called pseudoconformal integrals). We describe these novelties and their consequences in this Letter, and we make the full correlator and amplitude available as part of the Supplemental Material.

Yangian Symmetry of Scattering Amplitudes and the Dilatation Operator in N=4 Supersymmetric Yang-Mills Theory.

It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S matrix of N=4 super Yang-Mills theory. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only up to certain boundary terms found by Dolan, Nappi, and Witten. Using a result by Zwiebel, we show how the Yangian symmetry of the tree-level S matrix of N=4 super Yang-Mills theory implies precisely the Yangian invariance, up to boundary terms, of the one-loop dilatation operator.