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Towards celestial chiral algebras of self-dual black holes

Giuseppe Bogna, Simon Heuveline

Abstract

In this note, we show that several self-dual spacetimes previously studied in the context of celestial and twisted holography arise as limits of a certain Taub-NUT AdS$_4$ metric, the Pedersen metric, in which their Mass, NUT charge and cosmological constant obey a self-duality relation. In particular, self-dual Taub-NUT, a singular double cover of Eguchi-Hanson space, Euclidean AdS$_4$, and non-compact $\mathbb{CP}^2$, which is conformally equivalent to Burns space, arise as special limits of the Pedersen metric. The Pedersen metric can be derived from a curved twistor space which we conjecture to arise from a backreaction of self-dual gravity in the presence of a cosmological constant when coupled to a defect operator wrapping a certain $\mathbb{CP}^1$ at infinity. The curved twistor space gives rise to a $2$-parameter deformation of the celestial symmetry algebra $Lw_\wedge$ which reduces to previously studied algebras in various limits.

Towards celestial chiral algebras of self-dual black holes

Abstract

In this note, we show that several self-dual spacetimes previously studied in the context of celestial and twisted holography arise as limits of a certain Taub-NUT AdS metric, the Pedersen metric, in which their Mass, NUT charge and cosmological constant obey a self-duality relation. In particular, self-dual Taub-NUT, a singular double cover of Eguchi-Hanson space, Euclidean AdS, and non-compact , which is conformally equivalent to Burns space, arise as special limits of the Pedersen metric. The Pedersen metric can be derived from a curved twistor space which we conjecture to arise from a backreaction of self-dual gravity in the presence of a cosmological constant when coupled to a defect operator wrapping a certain at infinity. The curved twistor space gives rise to a -parameter deformation of the celestial symmetry algebra which reduces to previously studied algebras in various limits.
Paper Structure (22 sections, 64 equations, 1 figure)

This paper contains 22 sections, 64 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Pedersen metric and its limits
  3. Self-dual Plebański-Demiański Spacetimes
  4. The Pedersen metric
  5. Relation to Mabuchi gravity
  6. Various limits
  7. Self-dual gravity on twistor space
  8. Deforming twistor space with a defect operator
  9. Self-dual Taub-NUT
  10. The Pedersen twistor space
  11. Celestial symmetries from twistor space
  12. More on the the Pedersen metric
  13. From the Plebański-Demiański to the Pedersen metric
  14. Various limits of the Pedersen metric
  15. Self-dual Taub-NUT
  16. ...and 7 more sections

Figures (1)

  • Figure 1: the Pedersen metric (yellow) has various limits: a singular double cover of Eguchi-Hanson space (orange), self-dual Taub-NUT (violet), $\widetilde{\mathbb{CP}}^2$ (blue), Euclidean AdS$_4$ (green), and $\mathbb{R}^4$ (red). $\nu^2<0$ makes up the prolate case while $\nu^2>0$ makes up the oblate case.