The holographic dual of the Penrose transform
Abstract We consider the holographic duality between type-A higher-spin gravity in AdS4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic dual to this transform, which translates between twis...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP01(2018)100 |
| _version_ | 1818118826697424896 |
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| author | Yasha Neiman |
| author_facet | Yasha Neiman |
| author_sort | Yasha Neiman |
| collection | DOAJ |
| description | Abstract We consider the holographic duality between type-A higher-spin gravity in AdS4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic dual to this transform, which translates between twistor functions and CFT sources and operators. We present a twistorial expression for the partition function, which makes global higher-spin symmetry manifest, and appears to automatically include all necessary contact terms. In this picture, twistor space provides a fully nonlocal, gauge-invariant description underlying both bulk and boundary spacetime pictures. While the bulk theory is handled at the linear level, our formula for the partition function includes the effects of bulk interactions. Thus, the CFT is used to solve the bulk, with twistors as a language common to both. A key ingredient in our result is the study of ordinary spacetime symmetries within the fundamental representation of higher-spin algebra. The object that makes these “square root” spacetime symmetries manifest becomes the kernel of our boundary/twistor transform, while the original Penrose transform is identified as a “square root” of CPT. |
| first_indexed | 2024-12-11T05:00:29Z |
| format | Article |
| id | doaj.art-a0f72af46af042a6b69a1a1a56da502b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-11T05:00:29Z |
| publishDate | 2018-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a0f72af46af042a6b69a1a1a56da502b2022-12-22T01:20:10ZengSpringerOpenJournal of High Energy Physics1029-84792018-01-012018116510.1007/JHEP01(2018)100The holographic dual of the Penrose transformYasha Neiman0Okinawa Institute of Science and TechnologyAbstract We consider the holographic duality between type-A higher-spin gravity in AdS4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic dual to this transform, which translates between twistor functions and CFT sources and operators. We present a twistorial expression for the partition function, which makes global higher-spin symmetry manifest, and appears to automatically include all necessary contact terms. In this picture, twistor space provides a fully nonlocal, gauge-invariant description underlying both bulk and boundary spacetime pictures. While the bulk theory is handled at the linear level, our formula for the partition function includes the effects of bulk interactions. Thus, the CFT is used to solve the bulk, with twistors as a language common to both. A key ingredient in our result is the study of ordinary spacetime symmetries within the fundamental representation of higher-spin algebra. The object that makes these “square root” spacetime symmetries manifest becomes the kernel of our boundary/twistor transform, while the original Penrose transform is identified as a “square root” of CPT.http://link.springer.com/article/10.1007/JHEP01(2018)100AdS-CFT CorrespondenceHigher Spin SymmetryHigher Spin GravityConformal Field Theory |
| spellingShingle | Yasha Neiman The holographic dual of the Penrose transform Journal of High Energy Physics AdS-CFT Correspondence Higher Spin Symmetry Higher Spin Gravity Conformal Field Theory |
| title | The holographic dual of the Penrose transform |
| title_full | The holographic dual of the Penrose transform |
| title_fullStr | The holographic dual of the Penrose transform |
| title_full_unstemmed | The holographic dual of the Penrose transform |
| title_short | The holographic dual of the Penrose transform |
| title_sort | holographic dual of the penrose transform |
| topic | AdS-CFT Correspondence Higher Spin Symmetry Higher Spin Gravity Conformal Field Theory |
| url | http://link.springer.com/article/10.1007/JHEP01(2018)100 |
| work_keys_str_mv | AT yashaneiman theholographicdualofthepenrosetransform AT yashaneiman holographicdualofthepenrosetransform |