Supersymmetry in the AdS/CFT Correspondence

TL;DR

This paper explores how three-dimensional anti de Sitter supergravity symmetries induce boundary transformations matching two-dimensional conformal supergravities, revealing deep connections between bulk and boundary theories.

Contribution

It demonstrates that boundary symmetry transformations in 3D supergravity correspond exactly to 2D conformal supergravities, clarifying the holographic relationship.

Findings

Boundary transformations match 2D conformal supergravities

Weyl and super Weyl transformations derived from 3D symmetries

Establishes a link between bulk supergravity and boundary conformal theories

Abstract

We study how local symmetry transformations of (p, q) anti de Sitter supergravities in three dimensions act on fields on the two-dimensional boundary. The boundary transformation laws are shown to be the same as those of two-dimensional (p, q) conformal supergravities for p, q \leq 2. Weyl and super Weyl transformations are generated from three-dimensional general coordinate and super transformations.