Recursion relations for graviton scattering amplitudes from Bose symmetry and bonus scaling laws

David A. McGady and Laurentiu Rodina
Phys. Rev. D 91, 105010 – Published 13 May 2015

Abstract

Modern on-shell S-matrix methods may dramatically improve our understanding of perturbative quantum gravity, but current foundations of on-shell techniques for general relativity still rely on off-shell Feynman diagram analysis. Here, we complete the fully on-shell proof of Schuster and Toro J. High Energy Phys. 06 (2009) 079] that the recursion relations of Britto, Cachazo, Feng, and Witten (BCFW) apply to relativity tree amplitudes. We do so by showing that the surprising requirement of “bonus” z2 scaling under a BCFW shift directly follows from Bose symmetry. Moreover, we show that amplitudes in generic theories subjected to BCFW deformations of identical particles necessarily scale as zeven. When applied to the color ordered expansions of Yang-Mills, this directly implies the improved behavior under nonadjacent gluon shifts. Using the same analysis, three-dimensional gravity amplitudes scale as z4, compared to the z1 behavior for conformal Chern-Simons matter theory.

  • Received 16 December 2014

DOI:https://doi.org/10.1103/PhysRevD.91.105010

© 2015 American Physical Society

Authors & Affiliations

David A. McGady* and Laurentiu Rodina

  • Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

  • *dmcgady@princeton.edu
  • lrodina@princeton.edu

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Issue

Vol. 91, Iss. 10 — 15 May 2015

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