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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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