On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes

Abstract

We present evidence that loop amplitudes in maximally supersymmetric $\mathcal{N}=4$ Yang-Mills (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full $\mathcal{N}=4$ SYM has only logarithmic singularities and is free of any poles at infinity---properties closely related to uniform transcendentality and the UV-finiteness of the theory. We also briefly comment on implications for maximal ($\mathcal{N}=8$) supergravity.

4 pages, 3 figures

References in corpus (4)

• New Relations for Gauge-Theory Amplitudes
• Three-Loop Superfiniteness of N=8 Supergravity
• 5 loops in 24/5 dimensions
• The Structure of Multiloop Amplitudes in Gauge and Gravity Theories

Cited by in corpus (29)

• Lectures on differential equations for Feynman integrals
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• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Baikov representations, intersection theory, and canonical Feynman integrals
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams
• Nonperturbative Negative Geometries: Amplitudes at Strong Coupling and the Amplituhedron
• Amplitudes at Infinity
• Full-color three-loop three-point form factors in N=4 SYM
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• A first look at the function space for planar two-loop six-particle Feynman integrals
• Cross-Order Integral Relations from Maximal Cuts
• The Loop Momentum Amplituhedron
• All-loop cuts from the Amplituhedron
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Non-planar BCFW Grassmannian Geometries
• Alphabet of one-loop Feynman integrals
• On-Shell Structures of MHV Amplitudes Beyond the Planar Limit
• Maximal transcendental weight contribution of scattering amplitudes
• 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
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• The Stratification of Rigidity
• Bipartite Graphs, On-Shell Diagrams, and Bipartite Field Theories: a Computational Package in Mathematica