RG-Flow, Gravity and the Cosmological Constant

TL;DR

This paper investigates how the effective gravitational action in warped compactifications behaves under scale transformations, showing that flat space solutions remain stable if the cosmological constant is canceled at high energies, due to a dynamical adjustment mechanism.

Contribution

It introduces a flow equation for the effective action in warped compactifications, linking RG trajectories to classical solutions and stability of flat space backgrounds.

Findings

Flat space backgrounds are stable under RG flow if the cosmological constant is canceled.

The effective action's extremum corresponds to a complete RG trajectory of solutions.

Vacuum energy from phase transitions is absorbed by warp factor dynamics.

Abstract

We study the low energy effective action $S$ of gravity, induced by integrating out gauge and matter fields, in a general class of Randall-Sundrum type string compactification scenarios with exponential warp factors. Our method combines dimensional reduction with the holographic map between between 5-d supergravity and 4-d large $N$ field theory. Using the classical supergravity approximation, we derive a flow equation of the effective action $S$ that controls its behavior under scale transformations. We find that as a result each extremum of $S$ automatically describes a complete RG trajectory of classical solutions. This implies that, provided the cosmological constant is canceled in the high energy theory, classical flat space backgrounds naturally remain stable under the RG-flow. The mechanism responsible for this stability is that the non-zero vacuum energy generated by possible phase transitions, is absorbed by a dynamical adjustment of the contraction rate of the warp factor.