The N $$ \mathcal{N} $$ = 2 supersymmetric w 1+∞ symmetry in the two-dimensional SYK models
Abstract We identify the rank (q syk + 1) of the interaction of the two-dimensional N $$ \mathcal{N} $$ = (2, 2) SYK model with the deformation parameter λ in the Bergshoeff, de Wit and Vasiliev (in 1991)’s linear W ∞ [λ] algebra via λ = 1 2 q syk + 1 $$ \lambda =\frac{1}{2\left({q}_{\mathrm{syk}}+1...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2022)115 |
| _version_ | 1818238958400700416 |
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| author | Changhyun Ahn |
| author_facet | Changhyun Ahn |
| author_sort | Changhyun Ahn |
| collection | DOAJ |
| description | Abstract We identify the rank (q syk + 1) of the interaction of the two-dimensional N $$ \mathcal{N} $$ = (2, 2) SYK model with the deformation parameter λ in the Bergshoeff, de Wit and Vasiliev (in 1991)’s linear W ∞ [λ] algebra via λ = 1 2 q syk + 1 $$ \lambda =\frac{1}{2\left({q}_{\mathrm{syk}}+1\right)} $$ by using a matrix generalization. At the vanishing λ (or the infinity limit of q syk), the N $$ \mathcal{N} $$ = 2 supersymmetric linear W ∞ N , N $$ {W}_{\infty}^{N,N} $$ [λ = 0] algebra contains the matrix version of known N $$ \mathcal{N} $$ = 2 W ∞ algebra, as a subalgebra, by realizing that the N-chiral multiplets and the N-Fermi multiplets in the above SYK models play the role of the same number of βγ and bc ghost systems in the linear W ∞ N , N $$ {W}_{\infty}^{N,N} $$ [λ = 0] algebra. For the nonzero λ, we determine the complete N $$ \mathcal{N} $$ = 2 supersymmetric linear W ∞ N , N $$ {W}_{\infty}^{N,N} $$ [λ] algebra where the structure constants are given by the linear combinations of two different generalized hypergeometric functions having the λ dependence. The weight-1, 1 2 $$ \frac{1}{2} $$ currents occur in the right hand sides of this algebra and their structure constants have the λ factors. We also describe the λ = 1 4 $$ \frac{1}{4} $$ (or q syk = 1) case in the truncated subalgebras by calculating the vanishing structure constants. |
| first_indexed | 2024-12-12T12:49:55Z |
| format | Article |
| id | doaj.art-e676531ac6f845ed8c5746dddeea033d |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-12T12:49:55Z |
| publishDate | 2022-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e676531ac6f845ed8c5746dddeea033d2022-12-22T00:24:01ZengSpringerOpenJournal of High Energy Physics1029-84792022-05-012022514310.1007/JHEP05(2022)115The N $$ \mathcal{N} $$ = 2 supersymmetric w 1+∞ symmetry in the two-dimensional SYK modelsChanghyun Ahn0Department of Physics, Kyungpook National UniversityAbstract We identify the rank (q syk + 1) of the interaction of the two-dimensional N $$ \mathcal{N} $$ = (2, 2) SYK model with the deformation parameter λ in the Bergshoeff, de Wit and Vasiliev (in 1991)’s linear W ∞ [λ] algebra via λ = 1 2 q syk + 1 $$ \lambda =\frac{1}{2\left({q}_{\mathrm{syk}}+1\right)} $$ by using a matrix generalization. At the vanishing λ (or the infinity limit of q syk), the N $$ \mathcal{N} $$ = 2 supersymmetric linear W ∞ N , N $$ {W}_{\infty}^{N,N} $$ [λ = 0] algebra contains the matrix version of known N $$ \mathcal{N} $$ = 2 W ∞ algebra, as a subalgebra, by realizing that the N-chiral multiplets and the N-Fermi multiplets in the above SYK models play the role of the same number of βγ and bc ghost systems in the linear W ∞ N , N $$ {W}_{\infty}^{N,N} $$ [λ = 0] algebra. For the nonzero λ, we determine the complete N $$ \mathcal{N} $$ = 2 supersymmetric linear W ∞ N , N $$ {W}_{\infty}^{N,N} $$ [λ] algebra where the structure constants are given by the linear combinations of two different generalized hypergeometric functions having the λ dependence. The weight-1, 1 2 $$ \frac{1}{2} $$ currents occur in the right hand sides of this algebra and their structure constants have the λ factors. We also describe the λ = 1 4 $$ \frac{1}{4} $$ (or q syk = 1) case in the truncated subalgebras by calculating the vanishing structure constants.https://doi.org/10.1007/JHEP05(2022)115Conformal and W SymmetryHigher Spin Symmetry |
| spellingShingle | Changhyun Ahn The N $$ \mathcal{N} $$ = 2 supersymmetric w 1+∞ symmetry in the two-dimensional SYK models Journal of High Energy Physics Conformal and W Symmetry Higher Spin Symmetry |
| title | The N $$ \mathcal{N} $$ = 2 supersymmetric w 1+∞ symmetry in the two-dimensional SYK models |
| title_full | The N $$ \mathcal{N} $$ = 2 supersymmetric w 1+∞ symmetry in the two-dimensional SYK models |
| title_fullStr | The N $$ \mathcal{N} $$ = 2 supersymmetric w 1+∞ symmetry in the two-dimensional SYK models |
| title_full_unstemmed | The N $$ \mathcal{N} $$ = 2 supersymmetric w 1+∞ symmetry in the two-dimensional SYK models |
| title_short | The N $$ \mathcal{N} $$ = 2 supersymmetric w 1+∞ symmetry in the two-dimensional SYK models |
| title_sort | n mathcal n 2 supersymmetric w 1 ∞ symmetry in the two dimensional syk models |
| topic | Conformal and W Symmetry Higher Spin Symmetry |
| url | https://doi.org/10.1007/JHEP05(2022)115 |
| work_keys_str_mv | AT changhyunahn thenmathcaln2supersymmetricw1symmetryinthetwodimensionalsykmodels AT changhyunahn nmathcaln2supersymmetricw1symmetryinthetwodimensionalsykmodels |