Discrete holomorphicity and quantized affine algebras

Yacine Ikhlef, Robert Andrew Weston, Michael Wheeler, Paul Zinn-Justin

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We consider non-local currents in the context of quantized affine algebras, following the construction introduced by Bernard and Felder. In the case of Uq(A1(1)) and Uq(A2(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.

Original languageEnglish
Article number265205
Pages (from-to)1-34
Number of pages35
JournalJournal of Physics A: Mathematical and Theoretical
Issue number26
Publication statusPublished - 5 Jul 2013


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