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Celestial holography: An asymptotic symmetry perspective

Laura Donnay

TL;DR

The article surveys how infinite‑dimensional asymptotic symmetries of flat spacetime, encoded in BMS and its extensions, constrain a celestial holographic description of quantum gravity. It builds a bridge from bulk Bondi–Sachs data and BMS charges to a 2d celestial CFT on the sphere, via celestial amplitudes, conformal primary wavefunctions, and shadow transforms. Key contributions include: organizing the phase space into hard/soft sectors with a nontrivial symplectic structure, deriving CCFT currents from soft fluxes, and showing how Ward identities give rise to CCFT OPEs and a celestial stress tensor, all while highlighting the emerging w_{1+∞} symmetry in the conformally soft sector. The work argues that asymptotic symmetries furnish a robust, UV‑independent organizing principle for celestial holography and offers a concrete dictionary linking bulk IR structure to boundary CCFT data, with implications for gravitational memory and infrared physics.

Abstract

We review the role that infinite-dimensional symmetries arising at the boundary of asymptotically flat spacetimes play in the context of the celestial holography program. Once recast into the language of conformal field theory, asymptotic symmetries provide key constraints on the sought-for celestial dual to quantum gravity in flat spacetimes.

Celestial holography: An asymptotic symmetry perspective

TL;DR

The article surveys how infinite‑dimensional asymptotic symmetries of flat spacetime, encoded in BMS and its extensions, constrain a celestial holographic description of quantum gravity. It builds a bridge from bulk Bondi–Sachs data and BMS charges to a 2d celestial CFT on the sphere, via celestial amplitudes, conformal primary wavefunctions, and shadow transforms. Key contributions include: organizing the phase space into hard/soft sectors with a nontrivial symplectic structure, deriving CCFT currents from soft fluxes, and showing how Ward identities give rise to CCFT OPEs and a celestial stress tensor, all while highlighting the emerging w_{1+∞} symmetry in the conformally soft sector. The work argues that asymptotic symmetries furnish a robust, UV‑independent organizing principle for celestial holography and offers a concrete dictionary linking bulk IR structure to boundary CCFT data, with implications for gravitational memory and infrared physics.

Abstract

We review the role that infinite-dimensional symmetries arising at the boundary of asymptotically flat spacetimes play in the context of the celestial holography program. Once recast into the language of conformal field theory, asymptotic symmetries provide key constraints on the sought-for celestial dual to quantum gravity in flat spacetimes.
Paper Structure (37 sections, 181 equations, 7 figures, 3 tables)

This paper contains 37 sections, 181 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Symmetries of asymptotically flat spacetimes
  3. Bondi-Sachs metric
  4. The BMS group and its modern extensions
  5. Focus on the extended BMS group
  6. BMS symmetries at every corner
  7. Spacelike infinity
  8. Timelike infinity
  9. On matching conditions
  10. BMS charges and fluxes
  11. Surface charges and fluxes
  12. Goldstone and radiative modes
  13. Symplectic structure
  14. BMS hard and soft fluxes
  15. Celestial holography
  16. ...and 22 more sections

Figures (7)

  • Figure 1: Penrose (conformal) diagram of flat spacetime (on the left) versus the one of Anti-de Sitter (AdS) case.
  • Figure 2: Penrose diagram of flat spacetime. The different disconnected boundaries are null infinity (future $\mathscr I^+$ and past $\mathscr I^-$ null infinity), timelike (future $i^+$ and past $i^-$) infinity and spatial infinity $i^0$). Null geodesics follow constant $u$ trajectories and transverse coordinates are denoted by $x^A=(z,{\bar{z}})$. In this diagram, every left-right pair of points at the same $r>0$ and $t$ corresponds to a two-sphere $S^2$, each pair being exchanged under the antipodal map on $S^2$.
  • Figure 3: Hyperbolic resolution of spatial infinity $i^0$ via dS$_3$ slices of $\mathbb R^{3,1}$.
  • Figure 4: Hyperbolic slicing of $\mathbb R^{3,1}$ for future (past) timelike infinity $i^+$ ($i^-$).
  • Figure 5: Non-conservation of surface charges $Q$ due to outgoing flux of radiation at $\mathscr I^+$Donnay:2022wvx.
  • ...and 2 more figures