Holographie renormalization group flow and the low-energy, strong coupling, large W limit

From the AdS/CFT correspondence, we learn that the classical evolution of supergravity in the bulk can be reduced to a renormalization group (RG-) flow equation for the dual low-energy, strongly coupled and large W gauge theory on the boundary. This result has been used to obtain interesting relations between the various terms in the gravitational part of the boundary effective action, in particular the terms that affect the cosmological constant. It is found that once the cosmological constant is canceled in the UV theory, the RG-flow symmetry of the boundary effective action automatically implies the existence of zero cosmological constant solutions that extend all the way into the IR. Given the standard (and well founded) contradiction between the RG-flow idea and the observational evidence of a small cosmological constant, this is considered to be important progress, albeit incomplete, towards the final solution. Motivated by this success, it would be interesting to see whether this RG stability extends outside the scope of strong 't Hooft coupling and the large N regime that are implicitly assumed in the de Boer-Verlinde-Verlinde Hamilton-Jacob formulation of the holographic RG-flow equations of the boundary theory. In this paper, we address this question, where we start first by identifying the modifications that are required in the Hamilton-Jacobi formulation of the bulk supergravity theory when the strong 't Hooft coupling and the large W limits are relaxed. Next, taking into account the leading order corrections in these parameters, we derive new bulk-boundary relations, from which one can read all the local terms in the boundary effective action. Finally, we use the resulting new constraints to examine whether the RG stability of the cosmological extends to the new coupling regime. It would be also interesting to use these constraints to study the Randall-Sundrum scenario in this case. ©2001 The American Physical Society.