Bridging Carrollian and Celestial Holography

TL;DR

This paper explores the holographic duality for 4D asymptotically flat spacetimes, connecting Carrollian and celestial holography through Ward identities and correlation functions.

Contribution

It introduces a coupled Carrollian field theory at null infinity with external sources, reproduces BMS flux laws, and relates Carrollian and celestial holography via integral transforms.

Findings

Sourced Ward identities match BMS flux-balance laws

Derived low-point correlation functions for Carrollian theories

Mapped Carrollian Ward identities to celestial operator constraints

Abstract

Gravity in $4d$ asymptotically flat spacetime constitutes the archetypal example of a gravitational system with leaky boundary conditions. Pursuing our analysis of [1], 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 non-conservation of the charges. In particular, we show that the sourced Ward identities of a conformal Carrollian field theory living at null infinity reproduce the BMS 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.