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AdS/CFT correspondence and geometry. (English) Zbl 1081.81085
Biquard, Olivier (ed.), AdS/CFT correspondence: Einstein metrics and their conformal boundaries. 73rd meeting of the theoretical physicists and mathematicians, Strasbourg, France, September 11–13, 2003. Zürich: European Mathematical Society (EMS) (ISBN 0-03719-013-2/pbk). IRMA Lectures in Mathematics and Theoretical Physics 8, 73-101 (2005).
Summary: 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.
For the entire collection see [Zbl 1062.81002].

MSC:
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83C47 Methods of quantum field theory in general relativity and gravitational theory
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