Lifting a Conformal Field Theory from D-Dimensional Flat Space to (D+1)-Dimensional Ads Space

TL;DR

This paper demonstrates how to derive a higher spin field theory in AdS space from a boundary conformal field theory, establishing the AdS/CFT correspondence to second order in the coupling.

Contribution

It provides a method to lift a conformal field theory from flat space to AdS space and proves the AdS/CFT correspondence for certain models to second order.

Findings

Higher spin field theory HS(4) derived from O(N) sigma model

AdS/CFT correspondence established to second order

Operator product expansions extended to AdS space

Abstract

A quantum field theory on Anti-de-Sitter space can be constructed from a conformal field theory on its boundary Minkowski space by an inversion of the holographic mapping. To do this the conformal field theory must satisfy certain constraints. The structure of operator product expansions is carried over to AdS space. We show that this method yields a higher spin field theory HS(4) from the minimal conformal O(N) sigma model in three dimensions. For these models AdS/CFT correspondence is hereby proved to second order in the coupling constant.