Evaluating the AdS dual of the critical O(N) vector model

TL;DR

This paper proposes a method to evaluate the AdS dual of the three-dimensional critical O(N) vector model using Legendre transforms, providing insights into bulk interactions and implications for higher spin theories.

Contribution

It introduces a novel approach to compute the AdS dual of the critical O(N) model via Legendre transforms relating UV and IR fixed points.

Findings

The cubic bulk self-interaction coupling vanishes.

The method successfully evaluates the minimal bulk action.

Implications for higher spin theories are discussed.

Abstract

We argue that the AdS dual of the three dimensional critical O(N) vector model can be evaluated using the Legendre transform that relates the generating functionals of the free UV and the interacting IR fixed points of the boundary theory. As an example, we use our proposal to evaluate the minimal bulk action of the scalar field that it is dual to the spin-zero ``current'' of the O(N) vector model. We find that the cubic bulk self interaction coupling vanishes. We briefly discuss the implications of our results for higher spin theories and comment on the bulk-boundary duality for subleading N.