Gravity loop integrands from the ultraviolet

Abstract

We demonstrate that loop integrands of (super-)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of non-trivial cases. In the integrand construction, all scaling conditions are homogeneous. Therefore, the only required information about the amplitude is its vanishing at particular points in momentum space. This homogeneous construction gives indirect evidence for a new geometric picture for graviton amplitudes similar to the one found for planar N=4 super Yang-Mills theory. We also show how the behavior at infinity is related to the scaling of tree-level amplitudes under certain multi-line chiral shifts which can be used to construct new recursion relations.

33 pages; Updated funding acknowledgements; Added many clarifying statements; Published version

References in corpus (31)

• New Relations for Gauge-Theory Amplitudes
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Classical Polylogarithms for Amplitudes and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Lectures on differential equations for Feynman integrals
• The Momentum Kernel of Gauge and Gravity Theories
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• D-dimensional unitarity cut method
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• E7(7) constraints on counterterms in N=8 supergravity
• Taming Tree Amplitudes In General Relativity
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• The No-Triangle Hypothesis for N=8 Supergravity
• 5 loops in 24/5 dimensions
• Stringy KLT relations, global symmetries, and E_7(7) violation
• On-shell constructibility of tree amplitudes in general field theories
• On duality symmetries of supergravity invariants
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Decoupling Supergravity from the Superstring
• Two-Loop Renormalization of Quantum Gravity Simplified
• UV considerations on scattering amplitudes in a web of theories
• Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Amplitudes at Infinity
• Building Bases of Loop Integrands
• Note on Soft Graviton theorem by KLT Relation
• Cancellation of Conformal and Chiral Anomalies in $N\ge 5$ supergravities
• Gravitons, Bose-symmetry, and Bonus-scaling

Cited by in corpus (6)

• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Non-planar BCFW Grassmannian Geometries
• Poles At Infinity in On-shell Diagrams
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Smooth Splitting and Zeros from On-Shell Recursion