RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 SIGMA: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (377 kB)
Full text: http://emis.mi.ras.ru/.../086
References: PDF file   HTML file

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
Language:

Citation: Mark A. Walton, “On Affine Fusion and the Phase Model”, SIGMA, 8 (2012), 086, 13 pp.

Citation in format AMSBIB
\Bibitem{Wal12} \by Mark~A.~Walton \paper On Affine Fusion and the Phase Model \jour SIGMA \yr 2012 \vol 8 \papernumber 086 \totalpages 13 \mathnet{http://mi.mathnet.ru/sigma763} \crossref{https://doi.org/10.3842/SIGMA.2012.086} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3007273} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000312378000001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84870050648} 

• http://mi.mathnet.ru/eng/sigma763
• http://mi.mathnet.ru/eng/sigma/v8/p86

 SHARE:

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
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
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
4. Urichuk A., Walton M.A., “Adjoint affine fusion and tadpoles”, J. Math. Phys., 57:6 (2016), 061702
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
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
•  Number of views: This page: 119 Full text: 15 References: 29