A note on the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ holographic dictionary
Abstract This is a long-overdue companion paper to [1]. We study the relation between sl(3|2) Chern-Simons supergravity on AdS3 and two-dimensional CFT’s with N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ symmetry. Specifically, we carry out a complete analysis of asymptotic symmetries in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2020)177 |
| _version_ | 1819299071633915904 |
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| author | Alejandra Castro Alberto Faraggi Israel Osorio |
| author_facet | Alejandra Castro Alberto Faraggi Israel Osorio |
| author_sort | Alejandra Castro |
| collection | DOAJ |
| description | Abstract This is a long-overdue companion paper to [1]. We study the relation between sl(3|2) Chern-Simons supergravity on AdS3 and two-dimensional CFT’s with N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ symmetry. Specifically, we carry out a complete analysis of asymptotic symmetries in a basis that makes the superconformal structure transparent, allowing us to establish the precise dictionary between currents and transformation parameters in the bulk and their boundary counterparts. We also discuss the incorporation of sources and display in full detail the corresponding holographic Ward identities. By imposing suitable hermiticity conditions on the CFT currents, we identify the superalgebra su(2, 1|1, 1) as the appropriate real form of sl(3|2) in Lorentzian signature. We take the opportunity to review some of the properties of the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ conformal algebra, including its multiplet structure, OPE’s and spectral flow invariance, correcting some minor typos present in the literature. |
| first_indexed | 2024-12-24T05:39:58Z |
| format | Article |
| id | doaj.art-7d015cc3aef34420bebf9e02d5bdd95d |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-24T05:39:58Z |
| publishDate | 2020-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-7d015cc3aef34420bebf9e02d5bdd95d2022-12-21T17:12:51ZengSpringerOpenJournal of High Energy Physics1029-84792020-12-0120201213910.1007/JHEP12(2020)177A note on the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ holographic dictionaryAlejandra Castro0Alberto Faraggi1Israel Osorio2Institute for Theoretical Physics, University of AmsterdamDepartamento de Ciencias Físicas, Facultad de Ciencias Exactas, Universidad Andrés BelloInstituto de Física, Pontificia Universidad Católica de ChileAbstract This is a long-overdue companion paper to [1]. We study the relation between sl(3|2) Chern-Simons supergravity on AdS3 and two-dimensional CFT’s with N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ symmetry. Specifically, we carry out a complete analysis of asymptotic symmetries in a basis that makes the superconformal structure transparent, allowing us to establish the precise dictionary between currents and transformation parameters in the bulk and their boundary counterparts. We also discuss the incorporation of sources and display in full detail the corresponding holographic Ward identities. By imposing suitable hermiticity conditions on the CFT currents, we identify the superalgebra su(2, 1|1, 1) as the appropriate real form of sl(3|2) in Lorentzian signature. We take the opportunity to review some of the properties of the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ conformal algebra, including its multiplet structure, OPE’s and spectral flow invariance, correcting some minor typos present in the literature.https://doi.org/10.1007/JHEP12(2020)177AdS-CFT CorrespondenceConformal and W SymmetryExtended Super- symmetryHigher Spin Gravity |
| spellingShingle | Alejandra Castro Alberto Faraggi Israel Osorio A note on the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ holographic dictionary Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry Extended Super- symmetry Higher Spin Gravity |
| title | A note on the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ holographic dictionary |
| title_full | A note on the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ holographic dictionary |
| title_fullStr | A note on the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ holographic dictionary |
| title_full_unstemmed | A note on the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ holographic dictionary |
| title_short | A note on the N $$ \mathcal{N} $$ = 2 super- W 3 $$ {\mathcal{W}}_3 $$ holographic dictionary |
| title_sort | note on the n mathcal n 2 super w 3 mathcal w 3 holographic dictionary |
| topic | AdS-CFT Correspondence Conformal and W Symmetry Extended Super- symmetry Higher Spin Gravity |
| url | https://doi.org/10.1007/JHEP12(2020)177 |
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