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Celestial Holography meets dS/CFT

Hideo Furugori, Naoki Ogawa, Sotaro Sugishita, Takahiro Waki

TL;DR

This work builds a concrete bridge between celestial holography and the dS/CFT correspondence by mapping QFTs from flat Euclidean space R^{D+2} to theories on S^{D+1} via a Weyl rescaling and a Fourier transform, followed by an analytic continuation to de Sitter space. It shows that late/early-time dS extrapolated operators O_Δ^± can be expressed as linear combinations of celestial operators O_Δ and their shadow counterparts, revealing a nontrivial mixing rather than a simple BDHM-type dictionary. Consistency checks at two and four points demonstrate that celestial amplitudes and cosmological correlators agree under this dictionary, supporting a unified framework for transferring techniques between celestial holography and dS/CFT. The results open avenues to import dS/CFT methods, such as the cosmological bootstrap and central charge analyses, into celestial holography and suggest refined dictionaries beyond naive extrapolations. Overall, the paper provides a systematic route to connect flat-space holography with cosmological holography, enabling cross-fertilization of computational tools and physical insights.

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.

Celestial Holography meets dS/CFT

TL;DR

This work builds a concrete bridge between celestial holography and the dS/CFT correspondence by mapping QFTs from flat Euclidean space R^{D+2} to theories on S^{D+1} via a Weyl rescaling and a Fourier transform, followed by an analytic continuation to de Sitter space. It shows that late/early-time dS extrapolated operators O_Δ^± can be expressed as linear combinations of celestial operators O_Δ and their shadow counterparts, revealing a nontrivial mixing rather than a simple BDHM-type dictionary. Consistency checks at two and four points demonstrate that celestial amplitudes and cosmological correlators agree under this dictionary, supporting a unified framework for transferring techniques between celestial holography and dS/CFT. The results open avenues to import dS/CFT methods, such as the cosmological bootstrap and central charge analyses, into celestial holography and suggest refined dictionaries beyond naive extrapolations. Overall, the paper provides a systematic route to connect flat-space holography with cosmological holography, enabling cross-fertilization of computational tools and physical insights.

Abstract

We provide a concrete link between celestial amplitudes and cosmological correlators. We first construct a map from quantum field theories (QFTs) in -dimensional Euclidean space to theories on the -dimensional sphere, through a Weyl rescaling and a Fourier transformation. An analytic continuation extends this map to a relation between QFTs in Minkowski spacetime and in de Sitter spacetime 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 . Our framework offers a systematic route to transfer computational techniques and physical insights between celestial holography and the dS/CFT correspondence.

Paper Structure

This paper contains 27 sections, 117 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. QFT on $\mathrm{S}^{D+1}$ from QFT on $\mathbb{R}^{D+2}$
  3. Free Field
  4. Interactions
  5. QFT in dS$_{D+1}$ from QFT in M$_{D+2}$
  6. Connection between Celestial and Cosmological Correlators
  7. Consistency Check for Correlation Functions
  8. Two-Point Functions
  9. Four-Point Function ($D=2$, $\phi^{4}$ interaction)
  10. Left-hand side
  11. Right-hand side
  12. Matching of both sides
  13. Conclusion
  14. Summary and Discussions
  15. Future directions
  16. ...and 12 more sections

Figures (3)

  • Figure 1: A schematic diagram illustrating how celestial holography meets the dS/CFT correspondence.
  • Figure 2: Penrose diagram of Minkowski space and the Milne slices. Red curves represent $\mathrm{EAdS}$ slices, and blue dotted curves represent $\mathrm{dS}$ slices. By performing the Fourier transformation, we obtain a picture of $\mathrm{EAdS}^++\mathrm{dS}+\mathrm{EAdS}^-$.
  • Figure 3: Deformation of the integral contour of the polar angle $\theta$ in the path-integral. The original contour is $0 \to \pi$ along the real axis. It is deformed into the contours $A, B, C$ (and the dotted lines, which can be ignored).