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On AdS$_4$ deformations of celestial symmetries

Roland Bittleston, Giuseppe Bogna, Simon Heuveline, Adam Kmec, Lionel Mason, David Skinner

Abstract

Celestial holography has led to the discovery of new symmetry algebras arising from the study of collinear limits of perturbative gravity amplitudes in flat space. We explain from the twistor perspective how a non-vanishing cosmological constant $Λ$ naturally modifies the celestial chiral algebra. The cosmological constant deforms the Poisson bracket on twistor space, so the corresponding deformed algebra of Hamiltonians under the new bracket is automatically consistent. This algebra is equivalent to that recently found by Taylor and Zhu. We find a number of variations of the deformed algebra. We give the Noether charges arising from the expression of this algebra as a symmetry of the twistor action for self-dual gravity with cosmological constant.

On AdS$_4$ deformations of celestial symmetries

Abstract

Celestial holography has led to the discovery of new symmetry algebras arising from the study of collinear limits of perturbative gravity amplitudes in flat space. We explain from the twistor perspective how a non-vanishing cosmological constant naturally modifies the celestial chiral algebra. The cosmological constant deforms the Poisson bracket on twistor space, so the corresponding deformed algebra of Hamiltonians under the new bracket is automatically consistent. This algebra is equivalent to that recently found by Taylor and Zhu. We find a number of variations of the deformed algebra. We give the Noether charges arising from the expression of this algebra as a symmetry of the twistor action for self-dual gravity with cosmological constant.
Paper Structure (15 sections, 1 theorem, 38 equations)

This paper contains 15 sections, 1 theorem, 38 equations.

Table of Contents

  1. Introduction
  2. Twistors for AdS4
  3. The infinity twistor and Poisson structure
  4. The non-linear graviton with cosmological constant
  5. Symmetries and gravitons
  6. Elements of ham(C2xC*) as gravitons
  7. Celestial chiral algebras as vertex algebras
  8. Variations and extensions
  9. Symmetries of the twistor action
  10. Conclusion and discussion
  11. Twistor sigma models.
  12. Perturbiner calculations.
  13. Space-time realizations and AdS/CFT.
  14. Further deformations with $\Lambda \neq 0$.
  15. Quantum corrections.

Key Result

Theorem 1

There is a 1-to-1 correspondence between complex self-dual Einstein manifolds $(M,g)$ and deformations $\mathcal{PT}$ of a neighbourhood of a line in $\mathbb{PT}$ preserving $\{\cdot,\,\cdot\}_\Lambda$ as a Poisson structure with values in $\mathcal{O}(-2)$, the square root of the canonical bundle.

Theorems & Definitions (1)

  • Theorem 1: Ward '80