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 λNϕaϕa2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{\lambda }{N}{\left({\phi}^a{\phi}^a\right)}^2 $$\end{document} 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.