Do large $N$ free fermion or WZW theories have a holographic dual in $AdS_3/CFT_2$?

Question

I was wondering if for $N$ free Dirac fermions (or equivalently by bosonization, $N$ free bosons or an $SU(N)_1$ WZW theory plus an extra boson) have a holographic dual description via $AdS_3/CFT_2$?

If so, would the $SU(N)$ structure of the WZW theory be encoded in a transparent way in the dual bulk geometry?