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SIGMA, 2012, Volume 8, 086, 13 pages (Mi sigma763)  

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

Abstract: 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.

Keywords: affine fusion; phase model; integrable system; conformal field theory; noncommutative Schur polynomials; threshold level; higher-genus Verlinde dimensions.

DOI: https://doi.org/10.3842/SIGMA.2012.086

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Bibliographic databases:

ArXiv: 1208.0809
MSC: 81T40; 81R10; 81R12; 17B37; 17B81; 05E05
Received: August 1, 2012; in final form November 8, 2012; Published online November 15, 2012
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Citation: Mark A. Walton, “On Affine Fusion and the Phase Model”, SIGMA, 8 (2012), 086, 13 pp.

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Okuda S., Yoshida Yu., “G/G Gauged Wzw Model and Bethe Ansatz for the Phase Model”, J. High Energy Phys., 2012, no. 11, 146  crossref  mathscinet  isi  elib  scopus
    2. 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  crossref  isi  scopus
    3. 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  crossref  mathscinet  zmath  scopus
    4. Urichuk A., Walton M.A., “Adjoint affine fusion and tadpoles”, J. Math. Phys., 57:6 (2016), 061702  crossref  mathscinet  zmath  isi  scopus
    5. 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  crossref  mathscinet  zmath  scopus
    6. 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  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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