The N $$ \mathcal{N} $$ = 2, 4 supersymmetric linear W ∞[λ] algebras for generic λ parameter
Abstract The four different kinds of currents are given by the multiple (β, γ) and (b, c) ghost systems with a multiple product of derivatives. We determine their complete algebra where the structure constants depend on the deformation parameter λ appearing in the conformal weights of above fields n...
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| Natura: | Articolo |
| Lingua: | English |
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SpringerOpen
2024-02-01
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| Serie: | Journal of High Energy Physics |
| Soggetti: | |
| Accesso online: | https://doi.org/10.1007/JHEP02(2024)006 |
| _version_ | 1827214420845002752 |
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| author | Changhyun Ahn Man Hea Kim |
| author_facet | Changhyun Ahn Man Hea Kim |
| author_sort | Changhyun Ahn |
| collection | DOAJ |
| description | Abstract The four different kinds of currents are given by the multiple (β, γ) and (b, c) ghost systems with a multiple product of derivatives. We determine their complete algebra where the structure constants depend on the deformation parameter λ appearing in the conformal weights of above fields nontrivially and depend on the generic spins h 1 and h 2 appearing on the left hand sides in the (anti)commutators. By taking the linear combinations of these currents, the N $$ \mathcal{N} $$ = 4 supersymmetric linear W ∞ [λ] algebra (and its N $$ \mathcal{N} $$ = 4 superspace description) for generic λ is obtained explicitly. Moreover, we determine the N $$ \mathcal{N} $$ = 2 supersymmetric linear W ∞ [λ] algebra for arbitrary λ. As a by product, the λ deformed bosonic W 1+∞ [λ] × W 1+∞ λ + 1 2 $$ \left[\lambda +\frac{1}{2}\right] $$ subalgebra (a generalization of Pope, Romans and Shen’s work in 1990) is obtained. The first factor is realized by (b, c) fermionic fields while the second factor is realized by (β, γ) bosonic fields. The degrees of the polynomials in λ for the structure constants are given by (h 1 + h 2 – 2). Each w 1+∞ algebra from the celestial holography is reproduced by taking the vanishing limit of other deformation prameter q at λ = 0 with the contractions of the currents. |
| first_indexed | 2024-03-07T15:23:31Z |
| format | Article |
| id | doaj.art-1025bad67cc1419d92ed93c98fabc473 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2025-03-21T14:31:03Z |
| publishDate | 2024-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-1025bad67cc1419d92ed93c98fabc4732024-06-23T11:07:59ZengSpringerOpenJournal of High Energy Physics1029-84792024-02-012024215510.1007/JHEP02(2024)006The N $$ \mathcal{N} $$ = 2, 4 supersymmetric linear W ∞[λ] algebras for generic λ parameterChanghyun Ahn0Man Hea Kim1Department of Physics, Kyungpook National UniversityDepartment of Physics Education, Sunchon National UniversityAbstract The four different kinds of currents are given by the multiple (β, γ) and (b, c) ghost systems with a multiple product of derivatives. We determine their complete algebra where the structure constants depend on the deformation parameter λ appearing in the conformal weights of above fields nontrivially and depend on the generic spins h 1 and h 2 appearing on the left hand sides in the (anti)commutators. By taking the linear combinations of these currents, the N $$ \mathcal{N} $$ = 4 supersymmetric linear W ∞ [λ] algebra (and its N $$ \mathcal{N} $$ = 4 superspace description) for generic λ is obtained explicitly. Moreover, we determine the N $$ \mathcal{N} $$ = 2 supersymmetric linear W ∞ [λ] algebra for arbitrary λ. As a by product, the λ deformed bosonic W 1+∞ [λ] × W 1+∞ λ + 1 2 $$ \left[\lambda +\frac{1}{2}\right] $$ subalgebra (a generalization of Pope, Romans and Shen’s work in 1990) is obtained. The first factor is realized by (b, c) fermionic fields while the second factor is realized by (β, γ) bosonic fields. The degrees of the polynomials in λ for the structure constants are given by (h 1 + h 2 – 2). Each w 1+∞ algebra from the celestial holography is reproduced by taking the vanishing limit of other deformation prameter q at λ = 0 with the contractions of the currents.https://doi.org/10.1007/JHEP02(2024)006Conformal and W SymmetryExtended SupersymmetrySuperspaces |
| spellingShingle | Changhyun Ahn Man Hea Kim The N $$ \mathcal{N} $$ = 2, 4 supersymmetric linear W ∞[λ] algebras for generic λ parameter Journal of High Energy Physics Conformal and W Symmetry Extended Supersymmetry Superspaces |
| title | The N $$ \mathcal{N} $$ = 2, 4 supersymmetric linear W ∞[λ] algebras for generic λ parameter |
| title_full | The N $$ \mathcal{N} $$ = 2, 4 supersymmetric linear W ∞[λ] algebras for generic λ parameter |
| title_fullStr | The N $$ \mathcal{N} $$ = 2, 4 supersymmetric linear W ∞[λ] algebras for generic λ parameter |
| title_full_unstemmed | The N $$ \mathcal{N} $$ = 2, 4 supersymmetric linear W ∞[λ] algebras for generic λ parameter |
| title_short | The N $$ \mathcal{N} $$ = 2, 4 supersymmetric linear W ∞[λ] algebras for generic λ parameter |
| title_sort | n mathcal n 2 4 supersymmetric linear w ∞ λ algebras for generic λ parameter |
| topic | Conformal and W Symmetry Extended Supersymmetry Superspaces |
| url | https://doi.org/10.1007/JHEP02(2024)006 |
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