Celestial $Lw_{1+\infty}$ charges from a twistor action

TL;DR

This paper derives celestial $Lw_{1+ abla}$ charges in asymptotically flat spacetimes using twistor space, connecting symmetries to gravitational phase space and null infinity data.

Contribution

It provides a first-principle derivation of celestial symmetry generators from a twistor action, linking geometric and spacetime perspectives.

Findings

Charges expressed as surface integrals over celestial sphere

Connection established between twistor space and spacetime at null infinity

Symmetries shown to preserve asymptotic Bianchi identities

Abstract

The celestial $Lw_{1+\infty}$ symmetries in asymptotically flat spacetimes have a natural geometric interpretation on twistor space in terms of Poisson diffeomorphisms. Using this framework, we provide a first-principle derivation of the canonical generators associated with these symmetries starting from the Poisson BF twistor action for self-dual gravity. We express these charges as surface integrals over the celestial sphere in terms of spacetime data at null infinity. The connection between twistor space and spacetime expressions at $\mathscr{I}$ is achieved via an integral formula for the asymptotic Bianchi identities due to Bramson and Tod. Finally, we clarify how $Lw_{1+\infty}$ transformations are symmetries of gravity from a phase space perspective by showing the invariance of the asymptotic Bianchi identities.