Celestial holography meets dS/CFT

概要

Celestial holography reformulates scattering amplitudes in (D+2)-dimensional flat spacetime as correlation functions on the D-dimensional celestial sphere, while in (D+1)-dimensional de Sitter spacetime cosmological correlators are also viewed as correlation functions on the D-dimensional sphere at late times. Thus, both frameworks naturally lead to correlators on spheres with the same dimension. We provide a concrete map between celestial amplitudes and cosmological correlators through the dS foliation of (D+2)-dimensional flat spacetime. This gives a cosmological-celestial dictionary relating celestial operators to operators at future and past infinity in dS. In the dictionary, massless fields in Minkowski spacetime are mapped to fields with continuous mass spectra in dS. In particular, the modes associated with asymptotic symmetries in flat spacetime have precise counterparts on the de Sitter side. For U(1) gauge theory, the counterpart is the massless sector within the continuous Proca spectrum. For linearized gravity, supertranslations and superrotations are encoded, respectively, in partially massless and strictly massless sectors of a spin-2 field with continuous spectrum. Using these identifications, we find that the Ward-Takahashi identities of cosmological correlators reproduce the conformally soft photon and graviton theorems through the cosmological-celestial dictionary.

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