Higher spins and Yangian symmetries
Abstract The relation between the bosonic higher spin W ∞ λ $$ {\mathcal{W}}_{\infty}\left[\lambda \right] $$ algebra, the affine Yangian of g l 1 $$ \mathfrak{g}{\mathfrak{l}}_1 $$ , and the SHc algebra is established in detail. For generic λ we find explicit expressions for the low-lying W ∞ λ $$...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2017)152 |
| _version_ | 1818425046140452864 |
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| author | Matthias R. Gaberdiel Rajesh Gopakumar Wei Li Cheng Peng |
| author_facet | Matthias R. Gaberdiel Rajesh Gopakumar Wei Li Cheng Peng |
| author_sort | Matthias R. Gaberdiel |
| collection | DOAJ |
| description | Abstract The relation between the bosonic higher spin W ∞ λ $$ {\mathcal{W}}_{\infty}\left[\lambda \right] $$ algebra, the affine Yangian of g l 1 $$ \mathfrak{g}{\mathfrak{l}}_1 $$ , and the SHc algebra is established in detail. For generic λ we find explicit expressions for the low-lying W ∞ λ $$ {\mathcal{W}}_{\infty}\left[\lambda \right] $$ modes in terms of the affine Yangian generators, and deduce from this the precise identification between λ and the parameters of the affine Yangian. Furthermore, for the free field cases corresponding to λ = 0 and λ = 1 we give closed-form expressions for the affine Yangian generators in terms of the free fields. Interestingly, the relation between the W ∞ $$ {\mathcal{W}}_{\infty } $$ modes and those of the affine Yangian is a non-local one, in general. We also establish the explicit dictionary between the affine Yangian and the SHc generators. Given that Yangian algebras are the hallmark of integrability, these identifications should pave the way towards uncovering the relation between the integrable and the higher spin symmetries. |
| first_indexed | 2024-12-14T14:07:42Z |
| format | Article |
| id | doaj.art-1a236c736ded4c3fad65117aa0f2697b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T14:07:42Z |
| publishDate | 2017-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-1a236c736ded4c3fad65117aa0f2697b2022-12-21T22:58:25ZengSpringerOpenJournal of High Energy Physics1029-84792017-04-012017412910.1007/JHEP04(2017)152Higher spins and Yangian symmetriesMatthias R. Gaberdiel0Rajesh Gopakumar1Wei Li2Cheng Peng3Institut für Theoretische Physik, ETH ZurichInternational Centre for Theoretical Sciences-TIFRCAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of SciencesDepartment of Physics, Brown UniversityAbstract The relation between the bosonic higher spin W ∞ λ $$ {\mathcal{W}}_{\infty}\left[\lambda \right] $$ algebra, the affine Yangian of g l 1 $$ \mathfrak{g}{\mathfrak{l}}_1 $$ , and the SHc algebra is established in detail. For generic λ we find explicit expressions for the low-lying W ∞ λ $$ {\mathcal{W}}_{\infty}\left[\lambda \right] $$ modes in terms of the affine Yangian generators, and deduce from this the precise identification between λ and the parameters of the affine Yangian. Furthermore, for the free field cases corresponding to λ = 0 and λ = 1 we give closed-form expressions for the affine Yangian generators in terms of the free fields. Interestingly, the relation between the W ∞ $$ {\mathcal{W}}_{\infty } $$ modes and those of the affine Yangian is a non-local one, in general. We also establish the explicit dictionary between the affine Yangian and the SHc generators. Given that Yangian algebras are the hallmark of integrability, these identifications should pave the way towards uncovering the relation between the integrable and the higher spin symmetries.http://link.springer.com/article/10.1007/JHEP04(2017)152AdS-CFT CorrespondenceConformal and W SymmetryHigher Spin SymmetryQuantum Groups |
| spellingShingle | Matthias R. Gaberdiel Rajesh Gopakumar Wei Li Cheng Peng Higher spins and Yangian symmetries Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Higher Spin Symmetry Quantum Groups |
| title | Higher spins and Yangian symmetries |
| title_full | Higher spins and Yangian symmetries |
| title_fullStr | Higher spins and Yangian symmetries |
| title_full_unstemmed | Higher spins and Yangian symmetries |
| title_short | Higher spins and Yangian symmetries |
| title_sort | higher spins and yangian symmetries |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Higher Spin Symmetry Quantum Groups |
| url | http://link.springer.com/article/10.1007/JHEP04(2017)152 |
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