On RG-flow and the Cosmological Constant

TL;DR

This paper explores the relationship between RG flow and the cosmological constant within the AdS/CFT framework, deriving an effective action that satisfies a flow equation and admits flat or curved solutions.

Contribution

It constructs a low energy effective action obeying a Callan-Symanzik-type RG flow equation, linking RG flow to solutions of Einstein's equations with varying cosmological constants.

Findings

Flat spacetime solutions are generally allowed by the flow equation.

Non-zero cosmological constant solutions are also compatible with the flow.

The geometric interpretation relates to warped compactifications.

Abstract

The AdS/CFT correspondence implies that the effective action of certain strongly coupled large $N$ gauge theories satisfy the Hamilton-Jacobi equation of 5d 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 RG-flow equation. It follows from the flow equation that under quite general conditions the Einstein equations admit a flat space-time solution, but other solutions with non-zero cosmological constant are also allowed. I discuss the geometric interpretation of this result in the context of warped compactifications.