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Abstract We study the three dimensional O(N) invariant bosonic vector model with a λ N ϕ a ϕ a 2 $$ \frac{\lambda }{N}{\left({\phi}^a{\phi}^a\right)}^2 $$ interaction at its infrared fixed point, using a bilocal field approach and in an 1/N expansion. We identify a (negative energy squared) bound state in its spectrum about the large N conformal background. At the critical point this is identified with the Δ = 2 state. We further demonstrate that at the critical point the Δ = 1 state disappears from the spectrum.