Gravity On-shell Diagrams

Abstract

We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only $\dlog$-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for $\mathbb{N}=8$ supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum, poles at infinity are present and loop amplitudes show special behavior on certain collinear cuts. We demonstrate on 1-loop and 2-loop examples that the behavior on collinear cuts is a highly non-trivial property which requires cancellations between all terms contributing to the amplitude.

45 pages, 37 figures

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Cited by in corpus (34)

• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Gravity Amplitudes as Generalized Double Copies
• Prescriptive Unitarity
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Simple encoding of higher derivative gauge and gravity counterterms
• Loop-Level Double-Copy for Massive Quantum Particles
• Bootstrapping two-loop Feynman integrals for planar N=4 sYM
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Amplitudes at Infinity
• From 4d Ambitwistor Strings to On Shell Diagrams and Back
• On integrands and loop momentum in string and field theory
• Positive geometry, local triangulations, and the dual of the Amplituhedron
• UV cancelations in gravity loop integrands
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Building Bases of Loop Integrands
• MultivariateResidues: a Mathematica package for computing multivariate residues
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• Positive Geometries and Differential Forms with Non-Logarithmic Singularities I
• Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• On-shell diagrams and the geometry of planar N < 4 SYM theories
• BCFW-type recurrent relations for tree amplitudes of D=11 supergravity
• Gravity loop integrands from the ultraviolet
• An analytic superfield formalism for tree superamplitudes in D=10 and D=11
• Non-planar BCFW Grassmannian Geometries
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• $\Delta$-Algebra and Scattering Amplitudes
• New Worldsheet Formulae for Conformal Supergravity Amplitudes
• Poles At Infinity in On-shell Diagrams
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• Positivity, Grassmannian Geometry and Simplex-like Structures of Scattering Amplitudes
• Smooth Splitting and Zeros from On-Shell Recursion