Lecture notes on holographic renormalization. (English) Zbl 1044.83009

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.


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