Implications of nonplanar dual conformal symmetry

Abstract

Recently, Bern et al observed that a certain class of next-to-planar Feynman integrals possess a bonus symmetry that is closely related to dual conformal symmetry. It corresponds to a projection of the latter along a certain lightlike direction. Previous studies were performed at the level of the loop integrand, and a Ward identity for the integral was formulated. We investigate the implications of the symmetry at the level of the integrated quantities. In particular, we focus on the phenomenologically important case of five-particle scattering. The symmetry simplifies the four-variable problem to a three-variable one. In the context of the recently proposed space of pentagon functions, the symmetry is much stronger. We find that it drastically reduces the allowed function space, leading to a well-known space of three-variable functions. Furthermore, we show how to use the symmetry in the presence of infrared divergences, where one obtains an anomalous Ward identity. We verify that the Ward identity is satisfied by the leading and subleading poles of several nontrivial five-particle integrals. Finally, we present examples of integrals that possess both ordinary and dual conformal symmetry.

arXiv comment27 pages, 5 figures; typos corrected

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• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• An Operator Product Expansion for Form Factors
• 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
• Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes
• Exact scattering amplitudes in conformal fishnet theory
• Gravity loop integrands from the ultraviolet
• Non-planar BCFW Grassmannian Geometries
• Poles At Infinity in On-shell Diagrams
• SymBuild: a package for the computation of integrable symbols in scattering amplitudes
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Two-loop D-dimensional unitarity and dual conformal symmetry