The Tree Formula for MHV Graviton Amplitudes

Abstract

We present and prove a formula for the MHV scattering amplitude of n gravitons at tree level. Some of the more interesting features of the formula, which set it apart as being significantly different from many more familiar formulas, include the absence of any vestigial reference to a cyclic ordering of the gravitons--making it in a sense a truly gravitational formula, rather than a recycled Yang-Mills result, and the fact that it simultaneously manifests both S_{n-2} symmetry as well as large-z behavior that is O(1/z^2) term-by-term, without relying on delicate cancellations. The formula is seemingly related to others by an enormous simplification provided by O(n^n) iterated Schouten identities, but our proof relies on a complex analysis argument rather than such a brute force manipulation. We find that the formula has a very simple link representation in twistor space, where cancellations that are non-obvious in physical space become manifest.

18 pages, v2: note added

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• Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Scattering Amplitudes from Soft Theorems and Infrared Behavior
• A simple formula for gravitational MHV amplitudes
• Conformal and Einstein gravity from twistor actions
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Twistor Strings for N=8 Supergravity
• Constructing Amplitudes from Their Soft Limits
• Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Graphs, determinants and gravity amplitudes
• MHV scattering of gluons and gravitons in chiral strong fields
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• Tree-Level Formalism
• The Next-to-Simplest Quantum Field Theories
• UV cancelations in gravity loop integrands
• Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
• Superstring Amplitudes as a Mellin Transform of Supergravity
• Note on New KLT relations
• Kinematic Numerators and a Double-Copy Formula for N = 4 Super-Yang-Mills Residues
• Twistor actions for gauge theory and gravity
• Celestial Recursion
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
• Taming higher-derivative interactions and bootstrapping gravity with soft theorems
• Tree level amplitudes from soft theorems
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• A Link Representation for Gravity Amplitudes
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red
• A graphic approach to gauge invariance induced identity
• Gravitons, Bose-symmetry, and Bonus-scaling
• The n-point MHV one-loop Amplitude in N=4 Supergravity
• New expressions for gravitational scattering amplitudes
• Non-planar BCFW Grassmannian Geometries
• Poles At Infinity in On-shell Diagrams
• New Formulae for Gravity Amplitudes: Parity Invariance and Soft Limits
• The Twelve-Graviton Next-to-MHV Amplitude from Risager's Construction
• Constructing EYM amplitudes by inverse soft limit
• Evaluating EYM amplitudes in four dimensions by refined graphic expansion
• Gravity Amplitudes from n-Space
• Weighted Laplacians, cocycles and recursion relations
• Bonus scaling and BCFW in N=7 supergravity
• Pure connection formalism for gravity: Recursion relations
• Tree and $1$-loop fundamental BCJ relations from soft theorems
• Projectivity of Planar Zeros in Field and String Theory Amplitudes
• A note on multi-trace EYM amplitudes in four dimensions
• A simpler prescription for MHV graviton tree amplitudes in superstring theory
• Gravity Amplitudes from a Gaussian Matrix Model