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On renormalization-group flow and the cosmological constant

From the AdS-CFT correspondence we learn that the effective action of a strongly coupled large-N gauge theory satisfies the Hamilton-Jacobi equation of five-dimensional gravity. Using an analogy with the relativistic point particle, I construct a low-energy effective action that includes the Einstein action and obeys a Callan-Symanzik-type renormalization-group flow equation. The flow equation implies that under quite general conditions the Einstein equation admits a flat-spacetime solution, but other solutions with non-zero cosmological constant are also allowed. We discuss the geometric interpretation of this result in the context of warped compactifications. This contribution is an expansion of the talk presented at Strings '99 and is based on work by de Boer et al and Verlinde and Verlinde.