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

TL;DR

This paper establishes a theoretical framework connecting celestial holography and dS/CFT correspondence by mapping scalar and higher-spin fields between Minkowski and de Sitter spacetimes, and relates asymptotic symmetries to Ward-Takahashi identities.

Contribution

It extends the scalar dS/CFT map to fields with spin, identifies de Sitter counterparts of asymptotic symmetries, and derives celestial soft theorems from cosmological correlators.

Findings

Mapped scalar and higher-spin fields between Minkowski and de Sitter spacetimes.

Identified de Sitter counterparts of Minkowski asymptotic symmetries.

Reproduced celestial soft theorems from cosmological Ward-Takahashi identities.

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.