The AdS/CFT partition function, AdS as a lift of a CFT, and holographic RG flow from conformal deformations

TL;DR

This paper explores how conformal deformations, especially multitrace types, affect the AdS/CFT correspondence by developing a formalism that relates boundary deformations to bulk fields and interpreting the holographic RG flow as a scale-dependent process.

Contribution

It introduces a new formalism for constructing bulk fields from boundary operators under general conformal deformations, extending previous focus on double-trace deformations.

Findings

Replicated the holographic RG flow narrative independently.

Interpreted the regulating brane as a renormalization scale.

Explained the scale dependence of the boundary theory's spectrum.

Abstract

Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. Using this formalism, we independently replicate the holographic RG flow narrative to go on to interpret the brane used to regulate the AdS theory as a renormalization scale. The scale-dependence of the dilatation spectrum of a boundary theory in the presence of general deformations can be thus understood on the AdS side using this formalism.