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Bridging Carrollian and Celestial Holography

Laura Donnay, Adrien Fiorucci, Yannick Herfray, Romain Ruzziconi

TL;DR

This work develops a concrete bridge between Carrollian and celestial holography for 4d asymptotically flat spacetimes. It treats the non-conservation of asymptotic charges caused by radiation by introducing external sources and deriving sourced Ward identities in a 3d conformal Carrollian CFT, demonstrating that these identities encode the BMS flux-balance laws. A key technical advance is the introduction of the $oldsymbol{ash}$-transform (a Mellin-Fourier composite) that maps Carrollian boundary data to celestial CCFT operators, making precise how Carrollian Ward identities reproduce soft theorems in celestial holography. The paper also uncovers a new time-dependent branch in the two-point Carrollian correlator and shows how this and other Carrollian correlation structures map onto celestial correlation functions, providing a unified holographic picture and outlining future directions for explicit Carrollian CFT models at null infinity.

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.

Bridging Carrollian and Celestial Holography

TL;DR

This work develops a concrete bridge between Carrollian and celestial holography for 4d asymptotically flat spacetimes. It treats the non-conservation of asymptotic charges caused by radiation by introducing external sources and deriving sourced Ward identities in a 3d conformal Carrollian CFT, demonstrating that these identities encode the BMS flux-balance laws. A key technical advance is the introduction of the -transform (a Mellin-Fourier composite) that maps Carrollian boundary data to celestial CCFT operators, making precise how Carrollian Ward identities reproduce soft theorems in celestial holography. The paper also uncovers a new time-dependent branch in the two-point Carrollian correlator and shows how this and other Carrollian correlation structures map onto celestial correlation functions, providing a unified holographic picture and outlining future directions for explicit Carrollian CFT models at null infinity.

Abstract

Gravity in 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.
Paper Structure (62 sections, 298 equations, 4 figures, 1 table)

This paper contains 62 sections, 298 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Summary of the paper
  3. Organization of the paper
  4. Massless scattering in flat spacetime
  5. Bulk operators
  6. Massless fields in Minkowski spacetime and plane wave expansion
  7. Mellin transform and conformal primary basis
  8. Remark
  9. Boundary operators
  10. From bulk to boundary: the large-r expansion
  11. Remark
  12. From boundary to bulk: the Kirchhoff-d'Adhémar formula
  13. Remark
  14. From null infinity to the celestial sphere
  15. From position space to Mellin basis
  16. ...and 47 more sections

Figures (4)

  • Figure 1: Holographic nature of null infinity: two equivalent visions. $(i)$ On the left picture, $\mathscr{I}^+$ is seen as a boundary along which there is a Carrollian time evolution. This naturally leads to the Carrollian holography proposal where the putative dual theory is a $3d$ Carrollian CFT. This picture is well adapted to describe the dynamics of the system through the flux-balance laws encoding the non-conservation of the charges $Q$. $(ii)$ On the right picture, $\mathscr{I}^+$ is seen as a portion of a Cauchy hypersuface at late time. This naturally leads to the celestial holography proposal where the putative dual theory is a $2d$ CCFT. This second approach is particularly natural when considering a scattering process in flat spacetime.
  • Figure 2: Geometric implementation of the antipodal matching.
  • Figure 3: Interplay between the three bases of scattering in flat spacetime.
  • Figure 4: Time-ordered conformal boundary $\hat{\mathscr I}$ of asymptotically flat spacetimes.