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

TL;DR

This paper investigates the spectrum of a three-dimensional O(N) vector model at its infrared fixed point, revealing a bound state and spectrum changes at criticality using a bilocal field approach in the large N limit.

Contribution

It introduces a bilocal field method to analyze the spectrum of the O(N) model at the IR fixed point, identifying bound states and spectrum modifications at criticality.

Findings

Identified a negative energy squared bound state in the spectrum.

At the critical point, the $=2$ state is present, while the $=1$ state disappears.

The analysis was performed using a 1/N expansion and bilocal fields.

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.