Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons
The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons of any integer spin and propose an approach that allows one...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
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| Sprache: | English |
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Інститут математики НАН України
2010
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| Zitieren: | Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons / X. Bekaert, M. Grigoriev // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 59 назв. — англ. |
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Bekaert, X. Grigoriev, M. 2019-02-08T20:31:07Z 2019-02-08T20:31:07Z 2010 Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons / X. Bekaert, M. Grigoriev // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 59 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70S10; 51P05 DOI:10.3842/SIGMA.2010.038 https://nasplib.isofts.kiev.ua/handle/123456789/146315 The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons of any integer spin and propose an approach that allows one to have both locality and conformal symmetry manifest. This is achieved by using the ambient space representation in the fiber rather than in spacetime. This approach allows us to characterize a subalgebra of higher symmetries for any bosonic singleton, which is a candidate higher-spin algebra for mixed symmetry gauge fields on anti de Sitter spacetime. Furthermore, we argue that this algebra actually exhausts all higher symmetries. We are grateful to G. Barnich for collaboration on the initial stage of this project and to Universite Libre de Bruxelles and International Solvay Institutes for their kind hospitality while part of this work was being carried over. We are also grateful to A. Sergeev for some explanations of his works [57, 58]. X.B. acknowledges M.A. Vasiliev for helpful comments on his paper [25], M. Tsulaia for useful discussions, and especially N. Boulanger for early collaboration on manifestly conformal wave equations for singletons of integer spin. M.G. thanks G. Bonelli, E. Feigin, R. Metsaev and M.A. Vasiliev for discussions. The work of M.G. is supported by the RFBR grant 10-01-00408 and RFBR-CNRS grant 09-01-93105. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
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| title |
Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons |
| spellingShingle |
Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons Bekaert, X. Grigoriev, M. |
| title_short |
Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons |
| title_full |
Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons |
| title_fullStr |
Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons |
| title_full_unstemmed |
Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons |
| title_sort |
manifestly conformal descriptions and higher symmetries of bosonic singletons |
| author |
Bekaert, X. Grigoriev, M. |
| author_facet |
Bekaert, X. Grigoriev, M. |
| publishDate |
2010 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons of any integer spin and propose an approach that allows one to have both locality and conformal symmetry manifest. This is achieved by using the ambient space representation in the fiber rather than in spacetime. This approach allows us to characterize a subalgebra of higher symmetries for any bosonic singleton, which is a candidate higher-spin algebra for mixed symmetry gauge fields on anti de Sitter spacetime. Furthermore, we argue that this algebra actually exhausts all higher symmetries.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146315 |
| citation_txt |
Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons / X. Bekaert, M. Grigoriev // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 59 назв. — англ. |
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AT bekaertx manifestlyconformaldescriptionsandhighersymmetriesofbosonicsingletons AT grigorievm manifestlyconformaldescriptionsandhighersymmetriesofbosonicsingletons |
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2025-12-07T19:21:46Z |
| last_indexed |
2025-12-07T19:21:46Z |
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1850878518639984640 |