On the Holographic RG-flow and the Low-energy, Strong Coupling, Large N Limit

TL;DR

This paper explores the holographic renormalization group flow in the context of AdS/CFT, examining how corrections beyond the large N and strong coupling limit affect the stability of the cosmological constant and the boundary effective action.

Contribution

It derives new bulk/boundary relations incorporating 1/N and stringy corrections, analyzing their impact on RG-flow stability and the cosmological constant.

Findings

RG-stability of the cosmological constant may extend beyond strong coupling and large N regimes.

New relations between bulk and boundary terms are established including leading order corrections.

Implications for the Randall-Sundrum scenario are discussed.

Abstract

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.