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Is there any lattice model realization of the following model:

$c=1$ boson at the self-dual radius, or the $SU(2)$ WZW model at $k=1$.

This is a question inspired by: Orbifolds of the $c =1$ Bosonic theory on a circle

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    $\begingroup$ Please check spin-1/2 Heisenberg antiferromagnetic chain at zero temperature whose low-energy effective field theory is exactly SU(2) level 1 WZW model. For general SU(N) level k WZW models, there also exist their spin model partners. $\endgroup$
    – Yuan Yao
    Commented Dec 30, 2018 at 4:08

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