Celestial Holography meets dS/CFT

TL;DR

This paper establishes a concrete mathematical connection between celestial amplitudes and cosmological correlators by mapping quantum field theories across different spacetime geometries, enabling transfer of techniques between celestial holography and dS/CFT.

Contribution

It constructs a new map linking QFTs in Euclidean, Minkowski, and de Sitter spaces, unifying celestial holography with the dS/CFT correspondence.

Findings

Map from Euclidean QFTs to theories on the sphere

Extension of the map to Minkowski and de Sitter spacetimes

Representation of de Sitter operators on the celestial sphere

Abstract

We provide a concrete link between celestial amplitudes and cosmological correlators. We first construct a map from quantum field theories (QFTs) in $(D+2)$-dimensional Euclidean space to theories on the $(D+1)$-dimensional sphere, through a Weyl rescaling and a Fourier transformation. An analytic continuation extends this map to a relation between QFTs in Minkowski spacetime $\text{M}_{D+2}$ and in de Sitter spacetime $\text{dS}_{D+1}$ with the Bunch-Davies vacuum. Combining this relation with celestial holography, we show that the extrapolated operators in de Sitter space can be represented by operators on the celestial sphere $S^{D}$. Our framework offers a systematic route to transfer computational techniques and physical insights between celestial holography and the dS/CFT correspondence.