= Radius stabilization
{title2=$V\prime(R_0)=0,\quad m_R^2>0$}
<Radius stabilization> fixes the size of a <compactification> dynamically rather than choosing it as an undetermined parameter. If the four-dimensional <low-energy effective action> contains a <radion> $R$ with positive kinetic coefficient $Z(R)$ and <scalar potential> $V(R)$, a stable radius $R_0$ requires $V'(R_0)=0$ and $m_R^2=V''(R_0)/Z(R_0)>0$. This matters for the <hierarchy problem>: the volume or warp factor explains a hierarchy only if a consistent dynamics selects and maintains the required geometry.
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