Twistor action for full Einstein gravity

Develop and establish the status of a twistor action for full Einstein gravity suitable for extending the charge construction beyond the self-dual sector.

Background

The paper derives the charges using the Mason–Wolf twistor action for self-dual gravity and translates them to spacetime in a linearised setting. A formulation for full Einstein gravity would be needed to treat the non-self-dual bulk theory directly and to extend the phase-space analysis beyond the self-dual truncation.

Although the authors mention a possible route through conformal gravity restricted to Einstein modes, they explicitly state that the status of an appropriate twistor action for full Einstein gravity is unresolved.

References

Unlike the Yang-Mills case, the status of the twistor action for full Einstein gravity is not clear, although see for a route into the subject that restricts the twistor action for full conformal gravity to Einstein modes.

— AdS$_4$ Celestial Symmetries: from Ambitwistor charges to CFT$_3$ Light-Ray Operators  (2609.28633 - Goodenbour et al., 23 Sep 2026) in Outlook

Another important question concerns the Ward identities associated with these charges. Their conservation and interpretation as symmetry generators suggest an infinite family of Ward identities extending the usual conformal Ward identities. It would be important to establish their precise form and to determine whether they persist beyond the linearised or self-dual sectors.

— AdS$_4$ Celestial Symmetries: from Ambitwistor charges to CFT$_3$ Light-Ray Operators  (2609.28633 - Goodenbour et al., 23 Sep 2026) in Outlook