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 (1991 Nucl. Phys. B 365 98–120). In the case of and , these currents can be identified with configurations in the 6-vertex and Izergin–Korepin 19-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.