Bridging dS/CFT and Celestial Holography via Ward-Takahashi Identities

TL;DR

This work constructs a bridge between celestial holography and the dS/CFT framework by mapping a $(D{+}2)$-dimensional Minkowski theory to a $ ext{dS}_{D+1}$ theory with a continuous mass spectrum, and extends the cosmological-celestial dictionary to spin-1 and spin-2 fields. It shows how Minkowski asymptotic symmetries (supertranslations and superrotations) correspond to de Sitter boundary symmetries acting on partially massless and massless sectors, respectively, and demonstrates that the Ward-Takahashi identities of cosmological correlators reproduce the conformally soft photon and graviton theorems when translated into celestial CFT language. The paper also derives the celestial stress tensor from the late-time limit of gravitons in de Sitter space and discusses the emergence of a dual stress tensor, highlighting subtleties in current conservation on the celestial side. Overall, the results provide a unified holographic perspective that connects dS/CFT intuition with celestial holography and soft-theorem structures, with implications for the interpretation of celestial CFT data and the role of de Sitter boundary currents.

Abstract

In 2507.17558, we provide a map from a scalar theory on $(D+2)$-dimensional Minkowski spacetime to a scalar theory with a continuous mass spectrum on $(D+1)$-dimensional de Sitter spacetime, and propose a link between celestial amplitudes and cosmological correlators (the cosmological-celestial dictionary). We extend the construction to fields with spin 1 and 2, and find that massless spin fields map to spin fields with continuous mass spectra. In this construction, we identify the de Sitter counterparts of the Nambu-Goldstone modes associated with the asymptotic symmetries in Minkowski spacetime. For $U(1)$ gauge theories, the counterpart is restricted to the massless sector within the continuous Proca spectrum, while for linearized gravity supertranslations are encoded in the partially massless sector and superrotations in the strictly massless sector. Using the identification, we reveal that the associated Ward-Takahashi identities of the cosmological correlators reproduce the conformally soft photon and graviton theorems via the cosmological-celestial dictionary. In particular, the celestial stress tensor is derived from the asymptotic limit of gravitons in de Sitter spacetime.

Figures (1)

• Figure 1: A schematic diagram illustrating how celestial holography meets the dS/CFT correspondence Furugori:2025xkl.