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

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?

• I have also been looking for possible ${\rm AdS}_3$ duals of WZW models with ${\rm SU}(N)$ group. In particular I have found this paper today arxiv.org/abs/1011.5900. Still didn't read it but perhaps it contains what you are asking about.
– Gold
Jan 15, 2021 at 16:54