Topological Ward Identity and Anti-de Sitter Space/CFT Correspondence

TL;DR

This paper explores the duality between AdS space supergravity and superconformal field theories, demonstrating a topological Ward identity in 3D Chern-Simons gravity and discussing extensions to supersymmetric and higher-dimensional theories.

Contribution

It establishes a topological Ward identity as a key aspect of the AdS/CFT correspondence in three dimensions and discusses its potential extensions.

Findings

Topological Ward identity holds in 3D Chern-Simons gravity.

Duality can be interpreted through the topological Ward identity.

Extensions to supersymmetric and higher-dimensional theories are considered.

Abstract

The dual relationship between the supergravity in the anti-de Sitter(AdS) space and the superconformal field theory is discussed in the simplest form. We show that a topological Ward identity holds in the three dimensional Chern-Simons gravity. In this simple case the proposed dual relationship can be understood as the topological Ward identity. Extensions to the supersymmetric theories and higher dimensional ones are also briefly discussed.