AdS/CFT Duality and Holographic Renormalization Group: A Review

TL;DR

This review explores the AdS/CFT duality and holographic renormalization group, detailing supersymmetry, supergravity dual flows, and the holographic proof of the C-theorem, with focus on N=4 super Yang-Mills theory.

Contribution

It provides a comprehensive overview of holographic RG flows, supersymmetry, and the holographic proof of the C-theorem within the AdS/CFT framework, emphasizing N=4 super Yang-Mills theory.

Findings

Holographic derivation of RG flows in N=4 SYM

Holographic proof of the C-theorem

Discussion of Wilsonian holographic renormalization

Abstract

In this paper we review aspects of anti de Sitter/conformal field theory (AdS/CFT) duality and the notion of holographic renormalization group (RG) flow. We start by discussing supersymmetry and construct the N = 4 super Yang-Mills theory in d = 4 by Kaluza-Klein dimensional reduction method. Then, we study the large-N limit and how it leads to the AdS/CFT duality. Using AdS/CFT, we then study the super-gravitational dual flows to the RG flows in CFT generated by marginal and relevant deformations, using the N = 4 super Yang-Mills theory as an example. Then, we prove the Zamolodchikov C-theorem holographically. Finally, we discuss the Wilsonian holographic renormalization.