Gravity, Twistors and the MHV Formalism

Abstract

We give a self-contained derivation of the MHV amplitudes for gravity and use the associated twistor generating function to define a twistor action for the MHV diagram approach to gravity. Starting from a background field calculation on a spacetime with anti self-dual curvature, we obtain a simple spacetime formula for the scattering of a single, positive helicity linearized graviton into one of negative helicity. Re-expressing our integral in terms of twistor data allows us to consider a spacetime that is asymptotic to a superposition of plane waves. Expanding these out perturbatively yields the gravitational MHV amplitudes of Berends, Giele & Kuijf. We go on to take the twistor generating function off-shell at the perturbative level. Combining this with a twistor action for the anti self-dual background, we obtain a twistor action for the MHV diagram approach to perturbative gravity. We finish by extending these results to supergravity, in particular N=4 and N=8.

39 pages, 3 figures. Minor typos corrected, some clarification added

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• Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3
• Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
• Shifting Spin on the Celestial Sphere
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• A simple formula for gravitational MHV amplitudes
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• On Twistors and Conformal Field Theories from Six Dimensions
• From 4d Ambitwistor Strings to On Shell Diagrams and Back
• Higher-spin Yang-Mills, amplitudes and self-duality
• Superstring Amplitudes as a Mellin Transform of Supergravity
• Conformal Higher Spin Theory and Twistor Space Actions
• Gluon scattering on self-dual radiative gauge fields
• Note on New KLT relations
• Twistor actions for gauge theory and gravity
• A super MHV vertex expansion for N=4 SYM theory
• Twistor-strings and gravity tree amplitudes
• Towards the Gravituhedron: New Expressions for NMHV Gravity Amplitudes
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• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
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• New expressions for gravitational scattering amplitudes
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• Non-planar BCFW Grassmannian Geometries
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• Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity
• Constraining higher-spin S-matrices
• The Twelve-Graviton Next-to-MHV Amplitude from Risager's Construction
• New Formulae for Gravity Amplitudes: Parity Invariance and Soft Limits
• Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes
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• Weighted Laplacians, cocycles and recursion relations
• The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes
• Pure connection formalism for gravity: Recursion relations
• Projectivity of Planar Zeros in Field and String Theory Amplitudes
• A simpler prescription for MHV graviton tree amplitudes in superstring theory
• Gravity Amplitudes from a Gaussian Matrix Model
• Ambitwistor Yang-Mills Theory Revisited
• Superstring/Supergravity Mellin Correspondence in Grassmannian Formulation