### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Journal of High Energy Physics |

Volume | 4 |

Issue number | 8 PART A |

State | Published - Dec 1 2000 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- AdS-CFT Correspondance
- Renormalization Regularization and Renormalons
- Space-Time Symmetries

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## Cite this

*Journal of High Energy Physics*,

*4*(8 PART A), 1-15.