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

Abstract

We study the three dimensional O(N) invariant bosonic vector model with a $\frac{\lambda}{N}(\phi^{a}\phi^{a})^{2}$ 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 $\Delta=2$ state. We further demonstrate that at the critical point the $\Delta=1$ state disappears from the spectrum.