Special flow equation and GKP-Witten relation

TL;DR

This paper introduces a flow equation-based framework to reconstruct the bulk dual of a conformal field theory, demonstrating the emergence of AdS geometry and scalar fields satisfying the GKP-Witten relation.

Contribution

It develops a novel flow equation approach that reconstructs the bulk dual without prior assumptions, explicitly deriving AdS geometry and scalar fields in O(N) models.

Findings

AdS geometry emerges from the flow equation at a special parametrization.

Scalar fields satisfying the GKP-Witten relation are obtained.

The framework applies to O(N) vector models to reconstruct bulk duals.

Abstract

We develop a framework for the reconstruction of the bulk theory dual to conformal field theory (CFT) without any assumption by means of a flow equation. To this end we investigate a minimal extension of the free flow equation and find that at a special parametrization the conformal transformation for a normalized smeared operator exactly becomes the isometry of anti-de Sitter space (AdS). By employing this special flow equation to O$(N)$ vector models, we explicitly show that the AdS geometry as well as the scalar field satisfying the GKP-Witten relation concurrently emerge in this framework.