Light-cone formulation of conformal field theory adapted to AdS/CFT correspondence

TL;DR

The work addresses constructing a light-cone formulation for conformal fundamental and shadow fields in $d-1$ dimensions with arbitrary $\Delta$ and spin, including mixed-symmetry representations. It develops an $AdS$-friendly representation of the $SO(d-1,2)$ conformal algebra on CFT fields using spin operators and the $AdS$ mass operator $A$, with explicit expressions for generators and a basis change that cancels non-polynomial terms. Key contributions include a complete light-cone realization of the conformal algebra for arbitrary $\Delta$ and symmetry, the identification of $A,B$ with AdS-like defining relations, and a concrete AdS/CFT dictionary linking bulk solutions to boundary operators, plus a Euclidean two-point function result. The framework enables systematic study of AdS/CFT in massive arbitrary-spin sectors and mixed-symmetry conformal fields, providing a robust tool for cross-checks via correlators and enabling extensions to supersymmetric and higher-spin contexts.

Abstract

Light-cone formulation of conformal field theory in space-time of arbitrary dimension is developed. Conformal fundamental and shadow fields with arbitrary conformal dimension and arbitrary spin are studied. Representation of conformal algebra generators on space of conformal fundamental and shadow fields in terms of spin operators which enter in light-cone gauge formulation of field dynamics in AdS space is found. As an example of application of light-cone formalism we discuss AdS/CFT correspondence for massive arbitrary spin AdS fields and corresponding boundary CFT fields at the level of two point function.