Dual Conformal Structure Beyond the Planar Limit

TL;DR

This paper demonstrates that nonplanar integrals in $ ext{N}=4$ super-Yang--Mills theory exhibit dual conformal-like symmetries, extending known planar symmetries to a broader class of amplitudes and suggesting a universal underlying structure.

Contribution

It explicitly shows dual conformal-like symmetries in nonplanar integrals for two-loop four- and five-point amplitudes, proposing this symmetry extends to all amplitudes at any loop order.

Findings

Symmetries similar to dual conformal invariance are found in nonplanar integrals.

These symmetries apply to all subleading-color contributions at two loops.

The results suggest a universal symmetry structure in $ ext{N}=4$ super-Yang--Mills theory.

Abstract

The planar scattering amplitudes of $\mathcal{N} = 4$ super-Yang--Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at infinity. Recent work shows in various nontrivial examples that the simple analytic properties of the planar sector survive into the nonplanar sector, but this has yet to be understood from underlying symmetries. Here we explicitly show that for an infinite class of nonplanar integrals that covers all subleading-color contributions to the two-loop four- and five-point amplitudes of $\mathcal{N} = 4$ super-Yang--Mills theory, symmetries analogous to dual conformal invariance exist. A natural conjecture is that this continues to all amplitudes of the theory at any loop order.