Lecture notes on holographic renormalization. (English) Zbl 1044.83009

Skenderis, Kostas

Classical Quantum Gravity 19, No. 22, 5849-5876 (2002).

The paper consists of lecture notes reviewing the formalism of holographic renormalization. The author starts by discussing some mathematical results on asymptotically anti-de Sitter spacetimes. He then outlines the general method of holographic renormalization. This is illustrated in the case of a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalization action, holographic Ward identities, anomalies and renormalization group equations and the computation of renormlized one-, two-, and four-point functions. This is followed by a discussion of the application of the method to holographic renormalization group flows. He finishes by showing that the results of the near-boundary analysis of asymptotically anti-de Sitter spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes.

Reviewer: Oscar García-Prada (Madrid)

MSC:

83C45	Quantization of the gravitational field
81T15	Perturbative methods of renormalization applied to problems in quantum field theory

Keywords:

holographic renormalization; anti-de Sitter spacetimes; renormalization group