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On Affine Fusion and the Phase Model
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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On Affine Fusion and the Phase Model
Інший ID:
2010 Mathematics Subject Classification: 81T40; 81R10; 81R12; 17B37; 17B81; 05E05
DOI: http://dx.doi.org/10.3842/SIGMA.2012.086
DOI: http://dx.doi.org/10.3842/SIGMA.2012.086
Посилання:
On Affine Fusion and the Phase Model / M.A. Walton // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 19 назв. — англ.
Підтримка:
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.
Дата:
2012
Переглядів:
517
Завантажень:
243
Анотація:
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.
