On Affine Fusion and the Phase Model
A brief review is given of the integrable realization of affine fusion discovered recently by Korff and Stroppel. They showed that the affine fusion of the su(n) Wess-Zumino-Novikov-Witten (WZNW) conformal field theories appears in a simple integrable system known as the phase model. The Yang-Baxter...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148697 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Affine Fusion and the Phase Model / M.A. Walton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 19 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-148697 |
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Walton, M.A. 2019-02-18T17:56:45Z 2019-02-18T17:56:45Z 2012 On Affine Fusion and the Phase Model / M.A. Walton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T40; 81R10; 81R12; 17B37; 17B81; 05E05 DOI: http://dx.doi.org/10.3842/SIGMA.2012.086 https://nasplib.isofts.kiev.ua/handle/123456789/148697 A brief review is given of the integrable realization of affine fusion discovered recently by Korff and Stroppel. They showed that the affine fusion of the su(n) Wess-Zumino-Novikov-Witten (WZNW) conformal field theories appears in a simple integrable system known as the phase model. The Yang-Baxter equation leads to the construction of commuting operators as Schur polynomials, with noncommuting hopping operators as arguments. The algebraic Bethe ansatz diagonalizes them, revealing a connection to the modular S matrix and fusion of the su(n) WZNW model. The noncommutative Schur polynomials play roles similar to those of the primary field operators in the corresponding WZNW model. In particular, their 3-point functions are the su(n) fusion multiplicities. We show here how the new phase model realization of affine fusion makes obvious the existence of threshold levels, and how it accommodates higher-genus fusion. This paper is a contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”. The full collection is available at http://www.emis.de/journals/SIGMA/SESSF2012.html. I thank Elaine Beltaos, Terry Gannon, Ali Nassar and Andrew Urichuk for discussions and/or reading the manuscript. This research was supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Affine Fusion and the Phase Model Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On Affine Fusion and the Phase Model |
| spellingShingle |
On Affine Fusion and the Phase Model Walton, M.A. |
| title_short |
On Affine Fusion and the Phase Model |
| title_full |
On Affine Fusion and the Phase Model |
| title_fullStr |
On Affine Fusion and the Phase Model |
| title_full_unstemmed |
On Affine Fusion and the Phase Model |
| title_sort |
on affine fusion and the phase model |
| author |
Walton, M.A. |
| author_facet |
Walton, M.A. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
A brief review is given of the integrable realization of affine fusion discovered recently by Korff and Stroppel. They showed that the affine fusion of the su(n) Wess-Zumino-Novikov-Witten (WZNW) conformal field theories appears in a simple integrable system known as the phase model. The Yang-Baxter equation leads to the construction of commuting operators as Schur polynomials, with noncommuting hopping operators as arguments. The algebraic Bethe ansatz diagonalizes them, revealing a connection to the modular S matrix and fusion of the su(n) WZNW model. The noncommutative Schur polynomials play roles similar to those of the primary field operators in the corresponding WZNW model. In particular, their 3-point functions are the su(n) fusion multiplicities. We show here how the new phase model realization of affine fusion makes obvious the existence of threshold levels, and how it accommodates higher-genus fusion.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148697 |
| citation_txt |
On Affine Fusion and the Phase Model / M.A. Walton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 19 назв. — англ. |
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