The fuzzy-sphere regularization is an emerging numerical and theoretical technique for studying conformal field theories (CFTs). In this paper, we apply it to the $O\left(N\right)$ vector model, one of the most prominent theories for critical behavior in three space-time dimensions. We construct a model that realizes the $O\left(N\right)$ Wilson-Fisher and free-scalar CFTs for general $N$. For $N=2,3,4$, we present numerical evidence including the operator spectra and correlation functions in agreement with conformal symmetry and conformal bootstrap results.

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• Conformal field theory
• Critical phenomena
• Quantum Hall effect
• Quantum field theory
• Quantum many-body systems
• Exact diagonalization
• Landau-Ginzburg-Wilson theory