Twistor-strings and gravity tree amplitudes

Abstract

Recently we discussed how Einstein supergravity tree amplitudes might be obtained from the original Witten and Berkovits twistor-string theory when external conformal gravitons are restricted to be Einstein gravitons. Here we obtain a more systematic understanding of the relationship between conformal and Einstein gravity amplitudes in that twistor-string theory. We show that although it does not in general yield Einstein amplitudes, we can nevertheless obtain some partial twistor-string interpretation of the remarkable formulae recently been found by Hodges and generalized to all tree amplitudes by Cachazo and Skinner. The Hodges matrix and its higher degree generalizations encode the world sheet correlators of the twistor string. These matrices control both Einstein amplitudes and those of the conformal gravity arising from the Witten and Berkovits twistor-string. Amplitudes in the latter case arise from products of the diagonal elements of the generalized Hodges matrices and reduced determinants give the former. The reduced determinants arise if the contractions in the worldsheet correlator are restricted to form connected trees at MHV. The (generalized) Hodges matrices arise as weighted Laplacian matrices for the graph of possible contractions in the correlators and the reduced determinants of these weighted Laplacian matrices give the sum of of the connected tree contributions by an extension of the Matrix-Tree theorem.

32 pages, 3 figures. v2: many improvements to arguments and discussion; v3: improvements, expansions, and corrections to interpretation and discussion

References in corpus (6)

• Twistor Actions for Self-Dual Supergravities
• Heterotic twistor-string theory
• Conformal Supergravity Tree Amplitudes from Open Twistor String Theory
• Self-Dual Supergravity and Twistor Theory
• "Induced" N=4 conformal supergravity
• A Note on Graviton Amplitudes for New Twistor String Theories

Cited by in corpus (11)

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• The Kinematic Algebras from the Scattering Equations
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• Conformal and Einstein gravity from twistor actions
• On triviality of S-matrix in conformal higher spin theory
• Conformal higher spin scattering amplitudes from twistor space
• Conformal Higher Spin Theory and Twistor Space Actions
• Worldsheet factorization for twistor-strings
• Scattering of conformal higher spin fields
• On divergences in non-minimal N=4 conformal supergravity
• New Worldsheet Formulae for Conformal Supergravity Amplitudes