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Above two dimensions, all established interacting examples rely on supersymmetry, a symmetry between bosons and fermions, and whether any exist without it is unknown.","posed_since":"","precise":"A conformal manifold is a continuous family of CFTs generated by exactly marginal operators (scaling dimension exactly d along the family). In $d = 3\\ \\text{or}\\ 4$, determine whether a unitary interacting CFT without supersymmetry, at finite $N$, has an exactly marginal operator. Candidates come from holography: families of non-supersymmetric $\\mathrm{AdS}_4$ S-fold solutions of type IIB supergravity argued to be perturbatively and nonperturbatively stable (Giambrone et al. 2021; Bobev, Gautason, van Muiden 2023).","problem_ref":"018ea658fc92127621dc04f5886191593fbfbb84f2c6b026e984245f8eff7b9c","references":"","settled_by":"A non-supersymmetric CFT with an exactly marginal operator established at finite N by field theory or bootstrap, or a theorem excluding one under stated assumptions.","status_note":"Holographic $\\mathrm{AdS}4$ candidates (2021-2023) are argued stable, but no field-theory dual at finite $N$ has been identified.","title":"Do non-supersymmetric conformal manifolds exist above two 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