Celestial ₁₊∞ Symmetries from Twistor Space
We explain how twistor theory represents the self-dual sector of four-dimensional gravity in terms of the loop group of Poisson diffeomorphisms of the plane via Penrose's non-linear graviton construction. The symmetries of the self-dual sector are generated by the corresponding loop algebra ₁₊∞...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211529 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Celestial ₁₊∞ Symmetries from Twistor Space. Tim Adamo, Lionel Mason and Atul Sharma. SIGMA 18 (2022), 016, 23 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862561229538590720 |
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| author | Adamo, Tim Mason, Lionel Sharma, Atul |
| author_facet | Adamo, Tim Mason, Lionel Sharma, Atul |
| citation_txt | Celestial ₁₊∞ Symmetries from Twistor Space. Tim Adamo, Lionel Mason and Atul Sharma. SIGMA 18 (2022), 016, 23 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We explain how twistor theory represents the self-dual sector of four-dimensional gravity in terms of the loop group of Poisson diffeomorphisms of the plane via Penrose's non-linear graviton construction. The symmetries of the self-dual sector are generated by the corresponding loop algebra ₁₊∞ of the algebra ₁₊∞ of these Poisson diffeomorphisms. We show that these coincide with the infinite tower of soft graviton symmetries in tree-level perturbative gravity recently discovered in the context of celestial amplitudes. We use a twistor sigma model for the self-dual sector, which describes maps from the Riemann sphere to the asymptotic twistor space defined from characteristic data at null infinity I. We show that the OPE of the sigma model naturally encodes the Poisson structure on twistor space and gives rise to the celestial realization of ₁₊∞. The vertex operators representing soft gravitons in our model act as currents generating the wedge algebra of ₁₊∞ and produce the expected celestial OPE with hard gravitons of both helicities. We also discuss how the two copies of ₁₊∞, one for each of the self-dual and anti-self-dual sectors, are represented in the OPEs of vertex operators of the 4d ambitwistor string.
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| first_indexed | 2026-03-13T08:29:29Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211529 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T08:29:29Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
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| spelling | Adamo, Tim Mason, Lionel Sharma, Atul 2026-01-05T12:26:32Z 2022 Celestial ₁₊∞ Symmetries from Twistor Space. Tim Adamo, Lionel Mason and Atul Sharma. SIGMA 18 (2022), 016, 23 pages 1815-0659 2020 Mathematics Subject Classification: 83C60; 81U20; 32L25 arXiv:2110.06066 https://nasplib.isofts.kiev.ua/handle/123456789/211529 https://doi.org/10.3842/SIGMA.2022.016 We explain how twistor theory represents the self-dual sector of four-dimensional gravity in terms of the loop group of Poisson diffeomorphisms of the plane via Penrose's non-linear graviton construction. The symmetries of the self-dual sector are generated by the corresponding loop algebra ₁₊∞ of the algebra ₁₊∞ of these Poisson diffeomorphisms. We show that these coincide with the infinite tower of soft graviton symmetries in tree-level perturbative gravity recently discovered in the context of celestial amplitudes. We use a twistor sigma model for the self-dual sector, which describes maps from the Riemann sphere to the asymptotic twistor space defined from characteristic data at null infinity I. We show that the OPE of the sigma model naturally encodes the Poisson structure on twistor space and gives rise to the celestial realization of ₁₊∞. The vertex operators representing soft gravitons in our model act as currents generating the wedge algebra of ₁₊∞ and produce the expected celestial OPE with hard gravitons of both helicities. We also discuss how the two copies of ₁₊∞, one for each of the self-dual and anti-self-dual sectors, are represented in the OPEs of vertex operators of the 4d ambitwistor string. We are grateful to Andrew Strominger for discussions. TA is supported by a Royal Society University Research Fellowship and by the Leverhulme Trust (RPG-2020-386). LJM is supported in part by the STFC grant ST/T000864/1. AS is supported by a Mathematical Institute Studentship, Oxford, and by the ERC grant GALOP ID: 724638. We would also like to thank the SIGMA team for their courage and dedication, working through difficult circumstances in Kyiv in the face of the Russian invasion and aggression. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Celestial ₁₊∞ Symmetries from Twistor Space Article published earlier |
| spellingShingle | Celestial ₁₊∞ Symmetries from Twistor Space Adamo, Tim Mason, Lionel Sharma, Atul |
| title | Celestial ₁₊∞ Symmetries from Twistor Space |
| title_full | Celestial ₁₊∞ Symmetries from Twistor Space |
| title_fullStr | Celestial ₁₊∞ Symmetries from Twistor Space |
| title_full_unstemmed | Celestial ₁₊∞ Symmetries from Twistor Space |
| title_short | Celestial ₁₊∞ Symmetries from Twistor Space |
| title_sort | celestial ₁₊∞ symmetries from twistor space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211529 |
| work_keys_str_mv | AT adamotim celestial1symmetriesfromtwistorspace AT masonlionel celestial1symmetriesfromtwistorspace AT sharmaatul celestial1symmetriesfromtwistorspace |