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Lecture Notes on Holographic Renormalization
Classical and Quantum Gravity, 19 (22): 5849--5876 (11.10.2002)
DOI: 10.1088/0264-9381/19/22/306
Аннотация
We review the formalism of holographic renormalization. We start by
discussing mathematical results on asymptotically anti-de Sitter spacetimes. We
then outline the general method of holographic renormalization. The method is
illustrated by working all details in a simple example: a massive scalar field
on anti-de Sitter spacetime. The discussion includes the derivation of the
on-shell renormalized action, of holographic Ward identities, anomalies and RG
equations, and the computation of renormalized one-, two- and four-point
functions. We then discuss the application of the method to holographic RG
flows. We also show that the results of the near-boundary analysis of
asymptotically AdS spacetimes can be analytically continued to apply to
asymptotically de Sitter spacetimes. In particular, it is shown that the
Brown-York stress energy tensor of de Sitter spacetime is equal, up to a
dimension dependent sign, to the Brown-York stress energy tensor of an
associated AdS spacetime.
