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.

arXiv comment33 pages; Updated funding acknowledgements; Added many clarifying statements; Published version

References in corpus (100)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Multiloop integrals in dimensional regularization made simple
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Classical Polylogarithms for Amplitudes and Wilson Loops
• The Amplituhedron
• Magic identities for conformal four-point integrals
• One-Loop Amplitudes for e^+ e^- to Four Partons
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Lectures on differential equations for Feynman integrals
• On Tree Amplitudes in Gauge Theory and Gravity
• Progress in One-Loop QCD Computations
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Bootstrapping the three-loop hexagon
• The Momentum Kernel of Gauge and Gravity Theories
• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• D-dimensional unitarity cut method
• Explicit BCJ Numerators from Pure Spinors
• Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
• A direct proof of the CSW rules
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Uniqueness of two-loop master contours
• Into the Amplituhedron
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Positive Geometries and Canonical Forms
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• E7(7) constraints on counterterms in N=8 supergravity
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms
• Elliptic Feynman integrals and pure functions
• Taming Tree Amplitudes In General Relativity
• Unwinding the Amplituhedron in Binary
• Traintracks Through Calabi-Yaus: Amplitudes Beyond Elliptic Polylogarithms
• Unexpected Cancellations in Gravity Theories
• A (Bounded) Bestiary of Feynman Integral Calabi-Yau Geometries
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Positive Amplitudes In The Amplituhedron
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• Collinear and Soft Divergences in Perturbative Quantum Gravity
• String theory dualities and supergravity divergences
• The No-Triangle Hypothesis for N=8 Supergravity
• Soft Bootstrap and Supersymmetry
• Gravity Amplitudes as Generalized Double Copies
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Evidence for a Nonplanar Amplituhedron
• 5 loops in 24/5 dimensions
• The vanishing volume of D=4 superspace
• On-shell constructibility of tree amplitudes in general field theories
• Stringy KLT relations, global symmetries, and E_7(7) violation
• On duality symmetries of supergravity invariants
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Prescriptive Unitarity
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• Cuts from residues: the one-loop case
• The Momentum Amplituhedron
• Absence of Triangles in Maximal Supergravity Amplitudes
• The algebraic structure of cut Feynman integrals and the diagrammatic coaction
• The on-shell massless planar double box diagram with an irreducible numerator
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Decoupling Supergravity from the Superstring
• R^4 counterterm and E7(7) symmetry in maximal supergravity
• Simple Recursion Relations for General Field Theories
• Two-Loop Renormalization of Quantum Gravity Simplified
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Gravity On-shell Diagrams
• Cutting Deep Into The Amplituhedron
• UV considerations on scattering amplitudes in a web of theories
• Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
• Anomalies and divergences in N=4 supergravity
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Notes on Scattering Amplitudes as Differential Forms
• Dual Conformal Structure Beyond the Planar Limit
• Implications of nonplanar dual conformal symmetry
• Amplitudes at Infinity
• Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity
• On integrands and loop momentum in string and field theory
• UV cancelations in gravity loop integrands
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Building Bases of Loop Integrands
• Absence of U(1) Anomalous Superamplitudes in $\mathcal{N}\ge 5$ Supergravities
• Note on Soft Graviton theorem by KLT Relation
• Uniqueness from locality and BCFW shifts
• Cancellation of Conformal and Chiral Anomalies in $N\ge 5$ supergravities
• Gravitons, Bose-symmetry, and Bonus-scaling
• Two-loop n-point anomalous amplitudes in N=4 supergravity

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