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On Affine Fusion and the Phase Model

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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Main Author: Walton, M.A.
Format: Article
Language:English
Published: Інститут математики НАН України 2012
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/148697
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spelling irk-123456789-1486972019-02-19T01:30:47Z On Affine Fusion and the Phase Model Walton, M.A. 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. 2012 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148697 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Walton, M.A.
spellingShingle Walton, M.A.
On Affine Fusion and the Phase Model
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Walton, M.A.
author_sort Walton, M.A.
title On Affine Fusion and the Phase Model
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
publisher Інститут математики НАН України
publishDate 2012
url http://dspace.nbuv.gov.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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT waltonma onaffinefusionandthephasemodel
first_indexed 2023-05-20T17:30:59Z
last_indexed 2023-05-20T17:30:59Z
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