Colour-dressed hexagon tessellations for correlation functions and non-planar corrections

Abstract

Abstract We continue the study of four-point correlation functions by the hexagon tessellation approach initiated in [38] and [39]. We consider planar tree-level correlation functions in N=4 $$ \mathcal{N}=4 $$ 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 provide a direct interpretation of such wrapping processes in terms of N=2 $$ \mathcal{N}=2 $$ supersymmetric Feynman diagrams.

Keywords

• Integrable Field Theories
• 1/N Expansion
• AdS-CFT Correspondence
• Supersymmetric Gauge Theory