The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity

Abstract

We compute the symbol of the two-loop five-point amplitude in $\mathcal{N}=8$ supergravity. We write an ansatz for the amplitude whose rational prefactors are based on not only 4-dimensional leading singularities, but also $d$-dimensional ones, as the former are insufficient. Our novel $d$-dimensional unitarity-based approach to the systematic construction of an amplitude's rational structures is likely to have broader applications, for example to analogous QCD calculations. We fix parameters in the ansatz by performing numerical integration-by-parts reduction of the known integrand. We find that the two-loop five-point $\mathcal{N}=8$ supergravity amplitude is uniformly transcendental. We then verify the soft and collinear limits of the amplitude. There is considerable similarity with the corresponding amplitude for $\mathcal{N}=4$ super-Yang-Mills theory: all the rational prefactors are double copies of the Yang-Mills ones and the transcendental functions overlap to a large degree. As a byproduct, we find new relations between color-ordered loop amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory.

50 pages, 4 figures. v2: final journal version

References in corpus (31)

• New Relations for Gauge-Theory Amplitudes
• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Total positivity, Grassmannians, and networks
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Minimal Basis for Gauge Theory Amplitudes
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Three-Loop Superfiniteness of N=8 Supergravity
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• E7(7) constraints on counterterms in N=8 supergravity
• On the highest transcendentality in N=4 SUSY
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• Sharpening The Leading Singularity
• 5 loops in 24/5 dimensions
• On duality symmetries of supergravity invariants
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Two-Loop Renormalization of Quantum Gravity Simplified
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• The critical ultraviolet behaviour of N=8 supergravity amplitudes
• Two-Loop Gravity amplitudes from four dimensional Unitarity

Cited by in corpus (6)

• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• NNLO QCD corrections to three-photon production at the LHC
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• QCD and High Energy Interactions: MORIOND 2019 Theory Summary