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arXiv · 1302.4649

Discrete holomorphicity and quantized affine algebras

Y. Ikhlef·R. Weston·M. Wheeler·P. Zinn-Justin
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Abstract

We consider non-local currents in the context of quantized affine algebras, following the construction introduced by Bernard and Felder. In the case of $U_q(A_1^{(1)})$ and $U_q(A_2^{(2)})$, these currents can be identified with configurations in the six-vertex and Izergin--Korepin nineteen-vertex models. Mapping these to their corresponding Temperley--Lieb loop models, we directly identify non-local currents with discretely holomorphic loop observables. In particular, we show that the bulk discrete holomorphicity relation and its recently derived boundary analogue are equivalent to conservation laws for non-local currents.

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Y. Ikhlef, R. Weston, M. Wheeler, P. Zinn-Justin. 2013-02-19. Discrete holomorphicity and quantized affine algebras. https://doi.org/10.1088/1751-8113/46/26/265205

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