Scattering amplitudes in super-renormalizable gravity

  • Pietro Donà
  • Stefano Giaccari
  • Leonardo ModestoEmail author
  • Leslaw Rachwal
  • Yiwei Zhu
Open Access
Regular Article - Theoretical Physics


We explicitly compute the tree-level on-shell four-graviton amplitudes in four, five and six dimensions for local and weakly nonlocal gravitational theories that are quadratic in both, the Ricci and scalar curvature with form factors of the d’Alembertian operator inserted between. More specifically we are interested in renormalizable, super-renormalizable or finite theories. The scattering amplitudes for these theories turn out to be the same as the ones of Einstein gravity regardless of the explicit form of the form factors. As a special case the four-graviton scattering amplitudes in Weyl conformal gravity are identically zero. Using a field redefinition, we prove that the outcome is correct for any number of external gravitons (on-shell n−point functions) and in any dimension for a large class of theories. However, when an operator quadratic in the Riemann tensor is added in any dimension (with the exception of the Gauss-Bonnet term in four dimensions) the result is completely altered, and the scattering amplitudes depend on all the form factors introduced in the action.


Models of Quantum Gravity Classical Theories of Gravity 


Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Pietro Donà
    • 1
  • Stefano Giaccari
    • 1
  • Leonardo Modesto
    • 1
    Email author
  • Leslaw Rachwal
    • 1
  • Yiwei Zhu
    • 1
  1. 1.Department of Physics & Center for Field Theory and Particle PhysicsFudan UniversityShanghaiChina

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