Preprint 2017-07
Burkhard Eden, Yunfeng Jiang, Dennis le Plat, Alessandro Sfondrini
Colour-dressed hexagon tessellations for correlation functions and non-planar corrections.
Abstract: We continue the study of four-point correlation functions by the hexagon tes- sellation approach initiated in arXiv:1611.05436 and arXiv:1611.05577. We consider planar tree-level correlation functions in N = 4 supersymmetric Yang-Mills theory involving two non-protected operators. We find that, in order to reproduce the field theory result, it is necessary to include SU(N) colour factors in the hexagon formalism; moreover, we find that the hexagon approach as it stands is naturally tailored to the single-trace part of correlation functions, and does not account for multi-trace admixtures. We discuss how to compute correlators involving double-trace operators, as well as more general 1/N effects; in particular we compute the whole next-to-leading order in the large-N expansion of tree- level BMN two-point functions by tessellating a torus with punctures. Finally, we turn to the issue of “wrapping”, Lüscher-like corrections. We show that SU(N) colour-dressing reproduces an earlier empirical rule for incorporating single-magnon wrapping, and we pro- vide a direct interpretation of such wrapping processes in terms of N = 2 supersymmetric Feynman diagrams.
43 pp.