From Celestial Correlators to AdS, and back

TL;DR

This paper establishes a general relation between celestial correlators and Witten diagrams in EAdS space, enabling the use of EAdS techniques to analyze celestial correlators and their spectral properties.

Contribution

It introduces a perturbative relation between celestial correlators and EAdS Witten diagrams, facilitating the study of their analytic structure and unitarity constraints.

Findings

Spectral density in celestial correlators is meromorphic in the spectral parameter.

Contact processes correspond to contact Witten diagrams in EAdS.

Unitarity imposes positivity constraints on the spectral density.

Abstract

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