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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?

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  • $\begingroup$ 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. $\endgroup$
    – Gold
    Jan 15, 2021 at 16:54

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