Abstract
We present a general relation between celestial correlation functions in d-dimensions and Witten diagrams in (d + 1)-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(d + 1, 1). 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.
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Acknowledgments
CS and MT thank Andrea Puhm, Shu-Heng Shao and Kostas Skenderis for useful discussions and correspondence. CS and MT thank the Simons foundation for hospitality during the Symposium on Amplitudes Meet Cosmology 2022 and LI the TFI 2022 workshop of the INFN, where this work was presented. The research of CS was partially supported by the STFC grant ST/T000708/1. The research of MT was partially supported by the program “Rita Levi Montalcini” of the MIUR (Minister for Instruction, University and Research) and the INFN initiative STEFI.
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Iacobacci, L., Sleight, C. & Taronna, M. From celestial correlators to AdS, and back. J. High Energ. Phys. 2023, 53 (2023). https://doi.org/10.1007/JHEP06(2023)053
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DOI: https://doi.org/10.1007/JHEP06(2023)053