Bulk Local Operators, Conformal Descendants and Radial Quantization

TL;DR

This paper constructs bulk local operators in AdS using CFT at finite energy scale, revealing how bulk solutions naturally emerge from boundary field theory without prior bulk assumptions.

Contribution

It introduces a novel method to realize bulk local operators directly from boundary CFT considerations at finite energy scale, utilizing radial quantization.

Findings

Bulk local operators are constructed from CFT without prior bulk knowledge.

Normalizable solutions to bulk equations appear naturally in the boundary theory.

Regularization in radial quantization refines the initial construction.

Abstract

We establish a construction of the bulk local operators in AdS by considering CFT at finite energy scale. Without assuming any prior knowledge about the bulk, the normalizable solution to the bulk free field equation automatically appears in the field theory arguments. In the radial quantization formalism, we find a properly regularized version of our initial construction. Possible generalizations beyond pure AdS are also discussed.