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Whether this point is a consistent quantum theory for realistic N is unknown.","posed_since":"","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.","problem_ref":"eee838117fc834ffd707dff485f8bb9d14bb86714af6437138b52ce79d39b448","references":"","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.","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.","title":"Does an interacting unitary O(N) CFT exist in five 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