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On the holographic renormalization group. (English) Zbl 0989.81538
Summary: We propose a direct correspondence between the classical evolution equations of 5-d supergravity and the renormalization group (RG) equations of the dual 4-d large \(N\) gauge theory. Using standard Hamilton-Jacobi theory, we derive first order flow equations for the classical supergravity action \(S\), that take the usual form of the Callan-Symanzik equations, including the corrections due to the conformal anomaly. This result gives direct support for the identification of \(S\) with the quantum effective action of the gauge theory. In addition we find interesting new relations between the beta-functions and the counterterms that affect the 4-d cosmological and Newton constant.

MSC:
81T17 Renormalization group methods applied to problems in quantum field theory
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