标题： 高维膜模型中的模量稳定化 显示英文标题

标题： Moduli stabilization in higher dimensional brane models

摘要： 我们考虑了一类具有拓扑结构的扭曲高维膜模型$M \times \Sigma \times S^1/Z_2$，其中$\Sigma$是一个$D_2$维流形。两个余维数为一的膜嵌入到这种整体时空，并位于 orbifold 的不动点上。我们集中讨论一种情况，即指数型翘曲因子（依赖于沿 orbifold 方向的距离）伴随着闵可夫斯基时空$M$和内部空间$\Sigma$的度规线元。我们评估了这些模型中由整体标量场诱导的有效势，并表明通常情况下它可以稳定额外维度的大小。 作为应用，我们考虑了一种情景，即超对称性在截止尺度之下不远的地方被打破，并且电弱尺度与有效普朗克尺度之间的层次关系是由红移效应和大体积效应的组合生成的。后者由于负张力膜上的$\Sigma$收缩而变得高效，在此情形下，我们发现只要内部空间$\Sigma$是平坦的，有效势可以无需微调即可稳定额外维度的大小（以及层次关系）。 显示英文摘要

摘要： 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.