Celestial Lw1+∞ charges from a twistor action

A bstract The celestial Lw 1+ ∞ 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 $$ \mathcal{I} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>I</mml:mi> </mml:math> is achieved via an integral formula for the asymptotic Bianchi identities due to Bramson and Tod. Finally, we clarify how Lw 1+ ∞ transformations are symmetries of gravity from a phase space perspective by showing the invariance of the asymptotic Bianchi identities.