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arXiv · 1312.0956

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

Mark A. Walton
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Abstract

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.

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Mark A. Walton. 2013-12-03. Hopping in the Phase Model to a Non-Commutative Verlinde Formula for Affine Fusion. https://doi.org/10.1088/1742-6596%2F474%2F1%2F012033

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