On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity

Abstract

Exploiting singularities in Feynman integrals to get information about scattering amplitudes has been particularly useful at one-loop in theories where no triangles or bubbles appear. At higher loops the integrals possess subtle singularities. In this paper we give these singularities a physical interpretation and show how they turn tedious computations into purely pictorial manipulations. We illustrate our methods with various examples from the computation of four-particle amplitudes in N=4 super Yang-Mills and N=8 supergravity. Along the way we find clues towards an understanding i) of the rung-rule as a consequence of infra-red singularities, ii) of the non rung-rule integrals included in the basis as corrections to the rung-rule and iii) of the coefficients - including signs - of these two types of contribution. The role of corrections is to cancel unphysical singularities generically present in rung-rule integrals. A further byproduct, coming from the fact such unphysical singularities are located where conformal cross-ratios become unity, is the possibility of understanding the dual conformal invariance ansatz for constructing the basis of four-particle amplitudes in N=4 super Yang-Mills.

arXiv comment41 pages, 16 figures; references added, clarification added in section 6B

References in corpus (21)

• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• Magic identities for conformal four-point integrals
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Calculating Scattering Amplitudes Efficiently
• Three-Loop Superfiniteness of N=8 Supergravity
• On the Tree-Level S-Matrix of Yang-Mills Theory
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• The No-Triangle Hypothesis for N=8 Supergravity
• Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills
• Dissolving N=4 loop amplitudes into QCD tree amplitudes
• Infinities within graviton scattering amplitudes
• New Dual Conformally Invariant Off-Shell Integrals
• On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes
• The Effective Action of N=8 Supergravity

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• An Elliptic Yangian-Invariant, `Leading Singularity'
• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• 4-particle Amplituhedronics for 3-5 Loops
• Holonomies of gauge fields in twistor space 3: gravity as a square of N=4 theory
• Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Twistors, strings and supersymmetric gauge theories
• Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes