Discrete holomorphicity and quantized affine algebras

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.

References in corpus (1)

• Discretely holomorphic parafermions and integrable boundary conditions

Cited by in corpus (5)

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• Integrability as a consequence of discrete holomorphicity: loop models
• Conserved Currents in the Six-Vertex and Trigonometric Solid-On-Solid Models