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Single-minus graviton tree amplitudes are nonzero

Alfredo Guevara, Alexandru Lupsasca, David Skinner, Andrew Strominger, Kevin Weil

Abstract

Single-minus tree-level $n$-graviton scattering amplitudes are revisited. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. A Berends-Giele recursion relation for these amplitudes is derived and solved in a form involving a sum over trees. In a restricted kinematic decay region, this solution simplifies significantly to an $(n{-}2)$-fold product of soft factors. It is further shown in this region that, combined with suitable analyticity assumptions, the $n$-graviton amplitude is generated by a recursive $\mathcal{L}w_{1+\infty}$ Ward identity with the three-graviton amplitude as a seed.

Single-minus graviton tree amplitudes are nonzero

Abstract

Single-minus tree-level -graviton scattering amplitudes are revisited. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. A Berends-Giele recursion relation for these amplitudes is derived and solved in a form involving a sum over trees. In a restricted kinematic decay region, this solution simplifies significantly to an -fold product of soft factors. It is further shown in this region that, combined with suitable analyticity assumptions, the -graviton amplitude is generated by a recursive Ward identity with the three-graviton amplitude as a seed.
Paper Structure (24 sections, 74 equations)

This paper contains 24 sections, 74 equations.

Table of Contents

  1. Single-minus graviton amplitudes
  2. Lw(1+∞) bootstrap
  3. Chamber analyticity and the decay region
  4. Lw(1+∞) Ward identities
  5. Decay region amplitude
  6. Berends--Giele recursion
  7. Concrete examples
  8. Amplitudes in the chamber
  9. Vanishing of V in the chamber R(n,n-1)
  10. Evaluating V in the chamber R(n,n-1)
  11. Review of MHV amplitudes and Cayley trees
  12. Cayley tree formula.
  13. Regularized Cayley factors.
  14. Derivation from Berends--Giele recursion
  15. Unordered Berends--Giele recursion for gravity.
  16. ...and 9 more sections