Lattice model realization of $SU(2)$ WZW model at level $k$?

Question

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

This post imported from StackExchange Physics at 2020-11-09 09:43 (UTC), posted by SE-user annie marie heart

Comments

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.

This post imported from StackExchange Physics at 2020-11-09 09:43 (UTC), posted by SE-user Smart Yao