From celestial correlators to AdS, and back

We present a general relation between celestial correlation functions in $d$-dimensions and Witten diagrams $\left(d+1\right)$-dimensional Euclidean anti-de Sitter (EAdS) space, to all orders perturbation theory. Contact diagram processes are proportional contact diagrams, particle exchanges can be recast as continuum of EAdS where the exchanged particles carrying unitary Principal Series representations $SO\left(d+1,1\right)$. One then try import familiar techniques study properties correlators. In this work we use infer analytic structure spectral density conformal partial wave expansion correlators which, at least perturbatively, should meromorphic function parameter. also discuss non-perturbative constraints from unitarity Conformal Field Theory, which requires positivity density. This extends similar relations recently uncovered boundary de space EAdS, suggesting that could play central role efforts towards holography for lambdas.