Large N bilocals at the infrared fixed point of the three dimensional O(N) invariant vector theory with a quartic interaction

We study the three dimensional O(N) invariant bosonic vector model with a $\frac{\lambda }{N}({\varphi }^a{\varphi }^a{)}^2$ interaction at its infrared fixed point, using a bilocal field approach and in an $1\mathrm{/}N$ 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 $\mathrm{\Delta }=2$ state. We further demonstrate that at the critical point the $\mathrm{\Delta }=1$ state disappears from the spectrum.