  From the AdS/CFT correspondence, we learn that the classical evolution of
supergravity in the bulk can be reduced to a RG-flow equation for the dual
low-energy, strongly coupled and large N 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
term that affect the cosmological constant. It is found that once the
cosmological constant is cancelled 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 an 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 large N
regime that are implicitly assumed in the de Boer-Verlinde-Verlinde
Hamilton-Jacobi formulation of the holographic RG-flow equations of the
boundary theory. In this paper, we address this question. Taking into account
the leading order corrections in the 1/N and $\alpha'/{R^2}$ parameters, we
derive new bulk/boundary relations, from which one can read all the local terms
in the boundary effective action. Next, we use the resulting constraints, to
examine whether the RG-stability of the cosmological constant extends to the
new coupling regime. It would be also interesting to use these constraints to
study the Randall-Sundrum scenario in this case.
