Holographic reconstruction of gravitational perturbations in AdS/CFT and implications for celestial conformal field theory

A bstract We begin by reexamining the holographic reconstruction of scalar fields in four- dimensional anti-de Sitter spacetime, adopting a purely Lorentzian signature derivation, reproducing earlier results of HKLL and generalizing to arbitrary boundary metrics. The approach is extended to gravitational perturbations, focussing on perturbations around AdS 4 and show that the mapping can be formulated as a purely light-like integral of the conformal field theory stress energy tensor. An example is considered of relevance to the flat spacetime limit with nontrivial BMS charges turned on, potentially providing a quantum field theory definition of celestial CFT as a large central charge limit of a 3d CFT.