J. de Boer
- On the Holographic Renormalization Group
- The Journal of High Energy Physics
- Pages (from-to)
- Number of pages
- Document type
- Faculty of Science (FNWI)
- Institute for Theoretical Physics Amsterdam (ITFA)
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.
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