Symmetry Realization, Poisson Kernel and the AdS/CFT Correspondence

TL;DR

This paper explores symmetry realizations in AdS space, establishing the bulk-boundary propagator via the Poisson kernel, and demonstrates how it reproduces conformal correlators consistent with the AdS/CFT correspondence.

Contribution

It introduces a symmetry-based approach to AdS/CFT, utilizing the Poisson kernel to explicitly construct the bulk-boundary propagator and verify conformal invariance.

Findings

Bulk-boundary propagator derived from the Poisson kernel

Existence and uniqueness of the propagator proven

Correlators exhibit conformal invariance

Abstract

Two kinds of realizations of symmetry on classical domains or the Euclidean version of AdS space are used to study AdS/CFT correspondence. Mass of free particles is defined as an AdS group invariant, the Klein-Gordon and Dirac equations for relativistic particles in the AdS space are set up as a mimic in the case of Minkowskian space. The bulk-boundary propagator on the AdS space is given by the Poisson kernel. Theorems on the Poisson kernel guarantee the existence and sole of the bulk-boundary propagator. The propagator is used to calculate correlators of the theories that live on the boundary of the AdS space and show conformal invariance, which is desired by the AdS/CFT correspondence.