1302.4649 (Y. Ikhlef et al.)

Discrete holomorphicity and quantized affine algebras    [PDF]

Y. Ikhlef, R. Weston, M. Wheeler, P. Zinn-Justin

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.

View original: http://arxiv.org/abs/1302.4649