Massive fields in AdS from Constructive Holography

TL;DR

This paper develops a constructive approach within collective field theory to realize rotations in AdS spacetime, aligning with gravity theory and deriving eigenfunctions that inform the holographic duality.

Contribution

It introduces a method to implement rotations involving the holographic coordinate in collective field theory, matching gravity theory constructions and deriving key eigenfunctions.

Findings

Constructed rotations involving the holographic coordinate in collective field theory.

Aligned the construction with Metsaev's gravity theory approach.

Derived eigenfunctions of the AdS mass operator for holographic correspondence.

Abstract

Collective field theory offers a constructive framework for exploring the AdS/CFT duality. In this article, we focus on constructing rotations within the light-front quantized collective field theory for the full set of spatial coordinates in the dual bulk AdS spacetime. Two intricate aspects require attention: how rotations involving the emergent holographic coordinate are implemented, and how rotations that involve the spatial coordinates participating in the construction of the light-cone coordinates $X^{\pm}$ are realized. Our construction is in agreement with Metsaev's construction directly in the gravity theory. Additionally, we derive the eigenfunctions of the AdS mass operator, which dictate the GKPW rule for the emergent higher-dimensional theory.