Conserved gravitational charges, locality and the holographic Weyl anomaly - a fresh viewpoint

TL;DR

This paper reviews the derivation of conserved gravitational charges in asymptotically AdS spacetimes using covariant phase space methods, discussing their algebraic properties, locality, and implications for quantum theories within the holographic framework.

Contribution

It provides a fresh perspective on the definition and properties of conserved charges in AdS/CFT, emphasizing locality and addressing quantum aspects.

Findings

Clarifies the role of locality in conserved charge derivation.

Discusses the presence or absence of anomalies in charge algebra.

Connects classical charge definitions to quantum considerations.

Abstract

Since the proposal of the AdS/CFT correspondence, made by Maldacena and Witten, there has been some controversy about the definition of conserved Noether charges associated to asymptotic isometries in asymptotically AdS spacetimes, namely, whether they form an anomalous (i.e., a nontrivial central extension) representation of the Lie algebra of the conformal group in odd bulk dimensions or not. In the present work, we shall review the derivation of these charges by using covariant phase space techniques, emphasizing the principle of locality underlying it. We shall also comment on how these issues manifest themselves in the quantum setting.