AdS/CFT correspondence and Geometry

TL;DR

This paper introduces a Hamiltonian approach to holographic renormalization within the AdS/CFT framework, providing universal, covariant expressions for correlation functions and counterterms that improve efficiency over previous methods.

Contribution

It develops a novel Hamiltonian method for holographic renormalization, replacing standard near-boundary expansions with covariant ones organized by dilatation weight.

Findings

Universal expressions for counterterms derived

Covariant expansions replace near-boundary series

Method improves efficiency over previous approaches

Abstract

In the first part of this paper we provide a short introduction to the AdS/CFT correspondence and to holographic renormalization. We discuss how QFT correlation functions, Ward identities and anomalies are encoded in the bulk geometry. In the second part we develop a Hamiltonian approach to the method of holographic renormalization, with the radial coordinate playing the role of time. In this approach regularized correlation functions are related to canonical momenta and the near-boundary expansions of the standard approach are replaced by covariant expansions where the various terms are organized according to their dilatation weight. This leads to universal expressions for counterterms and one-point functions (in the presence of sources) that are valid in all dimensions. The new approach combines optimally elements from all previous methods and supersedes them in efficiency.