Constructing the bulk at the critical point of three-dimensional large $N$ vector theories

TL;DR

This paper demonstrates how, at the IR critical point of three-dimensional large N vector theories, the bulk higher spin spectrum simplifies by removing the scalar state, using a bilocal fields approach within the AdS/CFT framework.

Contribution

It shows the explicit construction of bulk higher spin fields at the IR critical point, highlighting the removal of the scalar state and providing a straightforward method from boundary bilocals.

Findings

Scalar state $=1$ removed from higher spin spectrum

Bulk variables derived from boundary bilocals via change of variables

Explicit Klein-Gordon higher spin Hamiltonians obtained

Abstract

In the context of the $AdS_{4}/CFT_{3}$ correspondence between higher spin fields and vector theories, we use the constructive bilocal fields based approach to this correspondence, to demonstrate, at the $IR$ critical point of the interacting vector theory and directly in the bulk, the removal of the $\Delta=1$ ($s=0$) state from the higher spins field spectrum, and to exhibit simple Klein-Gordon higher spin Hamiltonians. The bulk variables and higher spin fields are obtained in a simple manner from boundary bilocals, by the change of variables previously derived for the $UV$ critical point (in momentum space), together with a field redefinition.