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Title: Does an interacting unitary O(N) CFT exist in five dimensions
Plain: In five dimensions, a model of N-component spins may have a scale-invariant point that appears only at short distances. Whether this point is a consistent quantum theory for realistic N is unknown.
Precise: The $O(N)$ model in $4 < d < 6$ has a UV fixed point at large N, equivalently described by the cubic theory of Fei, Giombi and Klebanov. Determine whether for any finite N in $d = 5$ it is a unitary CFT, or whether it is non-unitary (complex or metastable) for all finite N through instanton effects; if unitary fixed points exist, find the smallest such N.
Settled by: Numerical bootstrap islands or exclusions for the 5D O(N) CFT as a function of N, consistent with large-N data, or a proof that nonperturbative instability persists at every finite N.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: contested
Status note: Large-$N$ and $6 - \epsilon$ expansions support existence at large $N$; bootstrap kinks are weak and instanton arguments (2019) suggest the fixed point is at best metastable.
Posed since: (empty)