Hopping in the Phase Model to a Non-Commutative Verlinde Formula for Affine Fusion

21st International Conference on Integrable Systems and Quantum Symmetries

Walton, M.A.^1

Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB T1K 3M4, Canada^1

关键词: Conformal field theories;    Fusion coefficients;    Hopping models;    Integrable models;    Non-commutative;    Phase model;    Schur polynomials;    Threshold levels;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012033/pdf
DOI  :  10.1088/1742-6596/474/1/012033

来源: IOP

【 摘 要 】

Korff and Stroppel discovered a realization of su(n) affine fusion, the fusion of the su(n) Wess-Zumino-Novikov-Witten (WZNW) conformal field theory, in the phase model, a limit of the q-boson hopping model. This integrable-model realization provides a new perspective on affine fusion, explored in a recent paper by the author. The role of WZNW primary fields is played in it by non-commutative Schur polynomials, and fusion coefficients are thus given by a non-commutative version of the Verlinde formula. We present the extension to all Verlinde dimensions, of arbitrary genus and any number N of points. The level-dependence of affine fusion is also discussed, using the concept of threshold level, and its generalization to threshold weight.