Light-cone form of field dynamics in anti-de Sitter space-time and AdS/CFT correspondence

TL;DR

This paper develops a light-cone formulation of field dynamics in anti-de Sitter space-time, establishing a precise correspondence between bulk fields and boundary operators within the AdS/CFT framework.

Contribution

It introduces explicit light-cone representations for AdS algebra generators and boundary conformal field theory, clarifying the bulk-boundary correspondence.

Findings

Explicit light-cone representations of AdS algebra generators.

Reformulation of boundary conformal field theory in light-cone form.

Establishment of a precise bulk-boundary correspondence in AdS/CFT.

Abstract

Light-cone form of field dynamics in anti-de Sitter space-time is developed. Using field theoretic and group theoretic approaches the light-cone representation for generators of anti-de Sitter algebra acting as differential operators on bulk fields is found. We also present light-cone reformulation of the boundary conformal field theory representations. Making use of these explicit representations of AdS algebra as isometry algebra in the bulk and the algebra of conformal transformations at the boundary a precise correspondence between the bulk fields and the boundary operators is established.