Abstract
In this follow up paper, we calculate higher point tree level graviton Witten diagrams in AdS4 via bulk perturbation theory. We show that by rearranging the bulk to bulk graviton propagators, the calculations effectively reduce to the computation of a scalar factor. Analogous to the amplitudes for vector boson interactions we computed in the previous paper, scalar factors for the graviton exchange diagrams also become relatively simple when written in momentum space. We explicitly calculate higher point correlators and discuss how this momentum space formalism makes flat space and collinear limits simpler.
Highlights
The study of the scattering amplitudes of gauge theories and gravity has revealed remarkably simple structures in flat space and has led to menagerie of basis such as twistors and geometric formulations like the amplituhedron [15,16,17,18,19]
Analogous to the amplitudes for vector boson interactions we computed in the previous paper, scalar factors for the graviton exchange diagrams become relatively simple when written in momentum space
The inflationary cosmology has stimulated a great deal of excitement in the study of late time de Sitter correlators [57,58,59,60] and we believe that the analogous calculations of momentum space AdS amplitudes can assist in the study of the shape of non-Gaussianities [36, 37, 53, 61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76]
Summary
We provide a brief review of momentum space bulk perturbation theory. In order to write a momentum space amplitude for a tree level Witten diagram, one needs to take the product of all relevant bulk to bulk and bulk to boundary propagators with the vertex factors, followed by an integration along the bulk radial direction.. This was given as part of the overall prescription in [56] without a detailed explanation. The permutations in the vertex are generated by the permutation group element (k1k2k3)(ikm)(jln) in cycle notation.9 This is analogous to the vertex factor for the vector boson in eq (2.1d) where the second and third terms can be obtained from the first one by the permutation (k1k2k3)(ijk) The permutations in the vertex are generated by the permutation group element (k1k2k3)(ikm)(jln) in cycle notation. This is analogous to the vertex factor for the vector boson in eq (2.1d) where the second and third terms can be obtained from the first one by the permutation (k1k2k3)(ijk)
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