Einstein supergravity amplitudes from twistor-string theory

Abstract

This paper gives a twistor-string formulation for all tree amplitudes of Einstein (super-)gravities for N=0 and 4. Formulae are given with and without cosmological constant and with various possibilities for the gauging. The formulae are justified by use of Maldacena's observation that conformal gravity tree amplitudes with Einstein wave functions and non-zero cosmological constant will correctly give the Einstein tree amplitudes. This justifies the construction of Einstein gravity amplitudes at N=0 from twistor-string theory and is extended to N=4 by requiring the standard relation between the MHV-degree and the degree of the rational curve for Yang-Mills; this systematically excludes the spurious conformal supergravity gravity contributions. For comparison, BCFW recursion is used to obtain twistor-string-like formulae at degree zero and one (anti-MHV and MHV) for amplitudes with N=8 supersymmetry with and without cosmological constant.

20 pages. v2: minor corrections & clarification of relation to formulae of Maldacena & Pimentel and Raju; v3: appendix on BCFW recursion added, published version. v4: Full derivation for 3 point MHV amplitude now included

References in corpus (13)

• Einstein Gravity from Conformal Gravity
• New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators
• Tree Level Recursion Relations In General Relativity
• Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3
• Twistor Actions for Self-Dual Supergravities
• Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects
• Heterotic twistor-string theory
• Tree-Level Amplitudes in N=8 Supergravity
• Conformal Supergravity Tree Amplitudes from Open Twistor String Theory
• Self-Dual Supergravity and Twistor Theory
• A Direct Proof of BCFW Recursion for Twistor-Strings
• A Note on Graviton Amplitudes for New Twistor String Theories
• Einstein Supergravity and New Twistor String Theories

Cited by in corpus (26)

• Ambitwistor strings in 4-dimensions
• Gravity from Rational Curves
• On duality of color and kinematics in (A)dS momentum space
• Perturbative gauge theory at null infinity
• Conformal and Einstein gravity from twistor actions
• Twistor Strings for N=8 Supergravity
• Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions
• Conformal higher spin scattering amplitudes from twistor space
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ II: Potentials
• Gravity with a cosmological constant from rational curves
• Conformal Higher Spin Theory and Twistor Space Actions
• Twistor actions for gauge theory and gravity
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ III: Contact Four-Point Amplitudes
• Self-Dual Conformal Gravity
• Twistor-strings and gravity tree amplitudes
• Worldsheet factorization for twistor-strings
• Scattering of conformal higher spin fields
• 3d conformal fields with manifest $sl(2,\mathbb{C})$
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• On divergences in non-minimal N=4 conformal supergravity
• New Worldsheet Formulae for Conformal Supergravity Amplitudes
• Conformal higher-spin symmetries in twistor string theory
• On Closed Twistor String Theory
• Soft Limits of Gluon and Graviton Correlators in Anti-de Sitter Space
• A Note on Classical Aspects of the Four Dimensional Anomaly-Free Twistor String