Dual Conformal Structure Beyond the Planar Limit

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.

arXiv comment5 pages, 3 figures

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Cited by in corpus (24)

• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Analytic result for a two-loop five-particle amplitude
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Implications of nonplanar dual conformal symmetry
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Dual conformal invariance for form factors
• UV cancelations in gravity loop integrands
• Building Bases of Loop Integrands
• Form factor recursion relations at loop level
• Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Exact scattering amplitudes in conformal fishnet theory
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• All-loop cuts from the Amplituhedron
• Constructing multi-loop scattering amplitudes with manifest singularity structure
• Gravity loop integrands from the ultraviolet
• Non-planar BCFW Grassmannian Geometries
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Two-loop D-dimensional unitarity and dual conformal symmetry
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons