Moduli instability in warped compactification - 4D effective theory approach

TL;DR

This paper analyzes moduli instability in warped compactifications using a 4D effective theory derived from 5D models, confirming the stability analysis and clarifying the relation between 4D and 5D solutions.

Contribution

It demonstrates that the 4D effective theory can reproduce exact 5D solutions and clarifies the origin of moduli instability using a new metric ansatz.

Findings

The exact solutions of Chen et al. are reproduced in the 4D effective theory.

The origin of moduli instability is identified within the 4D framework.

The paper refutes the claim that 4D solutions are more general than 5D solutions.

Abstract

We consider a 5D BPS dilatonic two brane model which reduces to the Randall-Sundrum model or the Horava-Witten theory for a particular choice of parameters. Recently new dynamical solutions were found by Chen et al., which describe a moduli instability of the warped geometry. Using a 4D effective theory derived by solving the 5D equations of motion, based on the gradient expansion method, we show that the exact solution of Chen et. al. can be reproduced within the 4D effective theory and we identify the origin of the moduli instability. We revisit the gradient expansion method with a new metric ansatz to clarify why the 4D effective theory solution can be lifted back to an exact 5D solution. Finally we argue against a recent claim that the 4D effective theory allows a much wider class of solutions than the 5D theory and provide a way to lift solutions in the 4D effective theory to 5D solutions perturbatively in terms of small velocities of the branes.