SIGMA, 2012, Volume 8, 086, 13 pages
This article is cited in 6 scientific papers (total in 6 papers)
On Affine Fusion and the Phase Model
Mark A. Walton
Department of Physics and Astronomy, University of Lethbridge,
Lethbridge, Alberta, T1K 3M4, Canada
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.
affine fusion; phase model; integrable system; conformal field theory; noncommutative Schur polynomials; threshold level; higher-genus Verlinde dimensions.
PDF file (377 kB)
MSC: 81T40; 81R10; 81R12; 17B37; 17B81; 05E05
Received: August 1, 2012; in final form November 8, 2012; Published online November 15, 2012
Mark A. Walton, “On Affine Fusion and the Phase Model”, SIGMA, 8 (2012), 086, 13 pp.
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Okuda S., Yoshida Yu., “G/G Gauged Wzw Model and Bethe Ansatz for the Phase Model”, J. High Energy Phys., 2012, no. 11, 146
Walton M.A., “Hopping in the Phase Model to a Non-Commutative Verlinde Formula for Affine Fusion”, Xxist international conference on integrable systems and quantum symmetries (isqs21), Journal of Physics Conference Series, 474, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2013
Ludmil Hadjiivanov, Paolo Furlan, “On the 2D Zero Modes’ Algebra of the SU(n) WZNW Model”, Springer Proceedings in Mathematics and Statistics, 111 (2014), 381–391
Urichuk A., Walton M.A., “Adjoint affine fusion and tadpoles”, J. Math. Phys., 57:6 (2016), 061702
Hadjiivanov, L.; Furlan; P., “Spread restricted young diagrams from a 2D WZNW dynamical quantum group”, Springer Proceedings in Mathematics and Statistics, 191 (2016), 501-510
L. Hadjiivanov, P. Furlan, “Quantum groups as generalized gauge symmetries in WZNW models. Part II. The quantized model”, Phys. Part. Nuclei, 48:4 (2017), 564–621
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