Intertwining Operator Realization of anti de Sitter Holography

TL;DR

This paper provides a group-theoretic framework for anti de Sitter holography, explicitly constructing boundary-to-bulk operators for arbitrary integer spins and revealing their intertwining properties, thus deepening the understanding of bulk-boundary correspondence.

Contribution

It introduces an explicit construction of boundary-to-bulk operators for all integer spins within representation theory, establishing their intertwining nature and the duality of boundary shadow fields.

Findings

Constructed boundary-to-bulk operators for arbitrary integer spins.

Demonstrated that these operators are intertwining operators.

Showed the existence of conjugate boundary shadow fields related by two-point functions.

Abstract

We give a group-theoretic interpretation of relativistic holography as equivalence between representations of the anti de Sitter algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the boundary-to-bulk operators for arbitrary integer spin the framework of representation theory. Further we show that these operators and the bulk-to-boundary operators are intertwining operators. In analogy to the de Sitter case, we show that each bulk field has two boundary (shadow) fields with conjugated conformal weights. These fields are related by another intertwining operator given by a two-point function on the boundary.