Conformal Symmetry of Supergravities in AdS spaces

TL;DR

This paper shows that applying the background field method to supergravity in AdS backgrounds yields a bulk path integral with conformal symmetry inherited from AdS isometries, which in turn induces rigid conformal invariance for boundary correlators. The authors derive bulk conformal symmetry and demonstrate its reduction to a simple rigid conformal group on the boundary, offering a symmetry-based foundation for aspects of the Maldacena AdS/CFT correspondence. They compare these symmetry results with established boundary 2- and 3-point calculations, discuss limitations in fixing all coefficients by symmetry alone, and highlight the role of bulk-to-bulk propagators in maintaining conformal covariance. Overall, the work clarifies how conformal symmetry naturally emerges in AdS supergravity and delineates what remains to be shown to achieve full duality with N=4 Yang-Mills theory.

Abstract

We show that the background field method applied to supergravity in adS space-time provides the path integral for the theory in the bulk with conformal symmetry associated with the isometry of the adS space. This in turn allows to establish the rigid conformal invariance of the generating functional for the supergravity correlators on the boundary.