Abstract
The bulk point singularity limit of conformal correlation functions in Lorentzian signature acts as a microscope to look into local bulk physics in AdS. From it we can extract flat space scattering processes localized in AdS that ultimate should be related to corresponding observables on the conformal field theory at the boundary. In this paper we use this interesting property to propose a map from flat space s-matrix to conformal correlation functions and try it on perturbative gravitational scattering. In particular, we show that the eikonal limit of gravitation scattering maps to a correlation function of the expected form at the bulk point singularity. We also compute the inverse map recovering a previous proposal in the literature.
Highlights
Another approach is to consider scattering processes that under certain conditions are very localized in the middle of AdS and are insensitive to the curvature of the space [3, 4, 28,29,30,31]
At the bulk point singularity, the conformal blocks are written in terms of spherical harmonic functions, and the operator product expansion (OPE) expansion of the correlation function adopts a similar form as an s-matrix partial wave expansion
By taking advanced of the all-loop resummation of gravitation scattering in flat space at the eikonal approximation,1 we can compute the corresponding resummation of the leading singularity expansion of Witten diagrams
Summary
We want to consider a four-point correlation function of primary scalar operators which for the sake of simplicity we take of having the same conformal dimension. Going back to the conformal partial wave expansion (2.4), at the bulk point singularity regime it has been argued in [30] that it should be dominated by large values of the exchanged operator conformal dimension. In order to use the proper OPE representation we need to analytically continue the euclidean conformal blocks to the lorentzian bulk point kinematics (2.7) and take the large ∆ limit, while keeping ξ∆−finite. This has been explicitly done in [32] and we borrow their result here, e−iπ∆. Where δ is the phase shift, which we are taken as complex such as the imaginary part corresponds to the inelasticity
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
