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

Adam Kmec; Lionel Mason; Romain Ruzziconi; Akshay Yelleshpur Srikant

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arXiv · 2407.04028

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

Adam Kmec·Lionel Mason·Romain Ruzziconi·Akshay Yelleshpur Srikant

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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.

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Adam Kmec, Lionel Mason, Romain Ruzziconi, Akshay Yelleshpur Srikant. 2024-07-04. Celestial $Lw_{1+\infty}$ charges from a twistor action. https://arxiv.org/abs/2407.04028

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