Moduli stabilization in higher dimensional brane models

TL;DR

This paper investigates how bulk scalar fields in higher-dimensional warped brane models can stabilize extra dimensions and generate the hierarchy between the electroweak and Planck scales without fine tuning, especially when the internal space is flat.

Contribution

It demonstrates that moduli stabilization can be achieved in warped higher-dimensional brane models through bulk scalar fields, with implications for hierarchy generation.

Findings

Moduli effective potential can stabilize extra dimensions.

Hierarchy between electroweak and Planck scales can be generated without fine tuning.

Stabilization is effective when the internal space is flat.

Abstract

We consider a class of warped higher dimensional brane models with topology $M \times \Sigma \times S^1/Z_2$, where $\Sigma$ is a $D_2$ dimensional manifold. Two branes of codimension one are embedded in such a bulk space-time and sit at the orbifold fixed points. We concentrate on the case where an exponential warp factor (depending on the distance along the orbifold) accompanies the Minkowski $M$ and the internal space $\Sigma$ line elements. We evaluate the moduli effective potential induced by bulk scalar fields in these models, and we show that generically this can stabilize the size of the extra dimensions. As an application, we consider a scenario where supersymmetry is broken not far below the cutoff scale, and the hierarchy between the electroweak and the effective Planck scales is generated by a combination of redshift and large volume effects. The latter is efficient due to the shrinking of $\Sigma$ at the negative tension brane, where matter is placed. In this case, we find that the effective potential can stabilize the size of the extra dimensions (and the hierarchy) without fine tuning provided that the internal space $\Sigma$ is flat.