A parafermionic hypergeometric function and supersymmetric 6j-symbols
We study properties of a parafermionic generalization of the hyperbolic hypergeometric function appearing as the most important part in the fusion matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev modular double. We show that this generalized hypergeometric function is a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-05-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321323000998 |
| _version_ | 1797842270288871424 |
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| author | Elena Apresyan Gor Sarkissian Vyacheslav P. Spiridonov |
| author_facet | Elena Apresyan Gor Sarkissian Vyacheslav P. Spiridonov |
| author_sort | Elena Apresyan |
| collection | DOAJ |
| description | We study properties of a parafermionic generalization of the hyperbolic hypergeometric function appearing as the most important part in the fusion matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev modular double. We show that this generalized hypergeometric function is a limiting form of the rarefied elliptic hypergeometric function V(r) and derive its transformation properties and a mixed difference-recurrence equation satisfied by it. At the intermediate level we describe symmetries of a more general rarefied hyperbolic hypergeometric function. An important r=2 case corresponds to the supersymmetric hypergeometric function given by the integral appearing in the fusion matrix of N=1 super Liouville field theory and the Racah-Wigner symbols of the quantum algebra Uq(osp(1|2)). We indicate relations to the standard Regge symmetry and prove some previous conjectures for the supersymmetric Racah-Wigner symbols by establishing their different parametrizations. |
| first_indexed | 2024-04-09T16:45:12Z |
| format | Article |
| id | doaj.art-e168842a602344ab9c9aaa3f4c5344e0 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-04-09T16:45:12Z |
| publishDate | 2023-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-e168842a602344ab9c9aaa3f4c5344e02023-04-23T06:05:43ZengElsevierNuclear Physics B0550-32132023-05-01990116170A parafermionic hypergeometric function and supersymmetric 6j-symbolsElena Apresyan0Gor Sarkissian1Vyacheslav P. Spiridonov2Yerevan Physics Institute, Alikhanian Br. 2, 0036 Yerevan, ArmeniaYerevan Physics Institute, Alikhanian Br. 2, 0036 Yerevan, Armenia; Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Moscow region, 141980, Russia; Corresponding author.Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Moscow region, 141980, Russia; National Research University Higher School of Economics, Moscow, RussiaWe study properties of a parafermionic generalization of the hyperbolic hypergeometric function appearing as the most important part in the fusion matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev modular double. We show that this generalized hypergeometric function is a limiting form of the rarefied elliptic hypergeometric function V(r) and derive its transformation properties and a mixed difference-recurrence equation satisfied by it. At the intermediate level we describe symmetries of a more general rarefied hyperbolic hypergeometric function. An important r=2 case corresponds to the supersymmetric hypergeometric function given by the integral appearing in the fusion matrix of N=1 super Liouville field theory and the Racah-Wigner symbols of the quantum algebra Uq(osp(1|2)). We indicate relations to the standard Regge symmetry and prove some previous conjectures for the supersymmetric Racah-Wigner symbols by establishing their different parametrizations.http://www.sciencedirect.com/science/article/pii/S0550321323000998 |
| spellingShingle | Elena Apresyan Gor Sarkissian Vyacheslav P. Spiridonov A parafermionic hypergeometric function and supersymmetric 6j-symbols Nuclear Physics B |
| title | A parafermionic hypergeometric function and supersymmetric 6j-symbols |
| title_full | A parafermionic hypergeometric function and supersymmetric 6j-symbols |
| title_fullStr | A parafermionic hypergeometric function and supersymmetric 6j-symbols |
| title_full_unstemmed | A parafermionic hypergeometric function and supersymmetric 6j-symbols |
| title_short | A parafermionic hypergeometric function and supersymmetric 6j-symbols |
| title_sort | parafermionic hypergeometric function and supersymmetric 6j symbols |
| url | http://www.sciencedirect.com/science/article/pii/S0550321323000998 |
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