Amplitudes at Infinity

Abstract

We investigate the asymptotically large loop-momentum behavior of multi-loop amplitudes in maximally supersymmetric quantum field theories in four dimensions. We check residue-theorem identities among color-dressed leading singularities in $\mathcal{N}=4$ supersymmetric Yang-Mills theory to demonstrate the absence of poles at infinity of all MHV amplitudes through three loops. Considering the same test for $\mathcal{N}=8$ supergravity leads us to discover that this theory does support non-vanishing residues at infinity starting at two loops, and the degree of these poles grow arbitrarily with multiplicity. This causes a tension between simultaneously manifesting ultraviolet finiteness---which would be automatic in a representation obtained by color-kinematic duality---and gauge invariance---which would follow from unitarity-based methods.

4+1+1 pages; 15 figures; details provided in ancillary Mathematica files

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Cited by in corpus (18)

• UV considerations on scattering amplitudes in a web of theories
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• All-Multiplicity Non-Planar MHV Amplitudes in sYM 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
• Manifestly Dual-Conformal Loop Integration
• Building Bases of Loop Integrands
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Gravity loop integrands from the ultraviolet
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Non-planar BCFW Grassmannian Geometries
• Poles At Infinity in On-shell Diagrams
• Illustrations of Integrand-Basis Building at Two Loops
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Locally Finite Observables in sYM
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Smooth Splitting and Zeros from On-Shell Recursion
• The Stratification of Rigidity