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The holographic renormalization group. (English) Zbl 1004.83049

From the text: In this lecture, we review the derivation of the holographic renormalization group given in [J. de Boer, E. Verlinde and H. Verlinde, J. High Energy Phys. 4, 15 p. (2000; Zbl 0989.81538)]. Some extra background material is included, and various applications are discussed.
A brief outline is as follows. We first review the AdS/CFT correspondence, in particular those features that are important in understanding the holographic renormalization group flow. Next, we briefly discuss these renormalization group flows and discuss a prototype flow, namely a domain wall solution. We then remind the reader of the basic idea of Hamilton-Jacobi theory in classical mechanics. We subsequently apply Hamilton-Jacobi theory to five-dimensional gravity coupled to scalar fields and explain how to extract from those the Callan-Symanzik equations of the dual field theory. We discuss some applications of this technique to the computation of the conformal anomaly, the cosmological constant problem and brane world scenarios. We conclude with some comments and by mentioning open problems.

MSC:

83E30 String and superstring theories in gravitational theory
81T17 Renormalization group methods applied to problems in quantum field theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory

Citations:

Zbl 0989.81538
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