Celestial $Lw_{1+\infty}$ charges from a twistor action
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910756645109760 |
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| author | Kmec, Adam Mason, Lionel Ruzziconi, Romain Srikant, Akshay Yelleshpur |
| author_facet | Kmec, Adam Mason, Lionel Ruzziconi, Romain Srikant, Akshay Yelleshpur |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Celestial $Lw_{1+\infty}$ charges from a twistor action Kmec, Adam Mason, Lionel Ruzziconi, Romain Srikant, Akshay Yelleshpur High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics 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. |
| title | Celestial $Lw_{1+\infty}$ charges from a twistor action |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2407.04028 |