Bridging Carrollian and celestial holography

Abstract

Gravity in 4d asymptotically flat spacetime constitutes the archetypal example of a gravitational system with leaky boundary conditions. Pursuing our previous analysis of [Carrollian Perspective on Celestial Holography, Phys. Rev. Lett. 129, 071602 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.071602], we argue that the holographic description of such a system requires the coupling of the dual theory living at null infinity to some external sources encoding the radiation reaching the conformal boundary and responsible for the nonconservation of the charges. In particular, we show that the sourced Ward identities of a conformal Carrollian field theory living at null infinity reproduce the Bondi-van der Burg-Metzner-Sachs flux-balance laws. We also derive the general form of low-point correlation functions for conformal Carrollian field theories and exhibit a new branch of solutions, which is argued to be the relevant one for holographic purposes. We then relate our Carrollian approach to the celestial holography proposal by mapping the Carrollian Ward identities to those constraining celestial operators through a suitable integral transform.