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

TL;DR

This work develops a comprehensive light-cone formalism for field dynamics in anti-de Sitter space-time and applies it to AdS/CFT correspondence. It constructs explicit light-cone representations of the AdS algebra as differential operators on bulk fields and reformulates boundary conformal transformations in the light-cone basis, using both field-theoretic and group-theoretic methods. Central to the framework are the AdS mass operator $A$, the spin operator $M^{IJ}$, and the relations that map bulk fields to boundary operators, including shadow operators for non-normalizable modes. The results provide a practical, algebraic route to state/operator matching for arbitrary spin, including totally symmetric, antisymmetric, and mixed-symmetry representations, with promising implications for higher-spin theories and strings in AdS backgrounds.

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.