Light Moduli in Almost No-Scale Models

We discuss the stabilization of the compact dimension for a class of five-dimensional orbifold supergravity models. Supersymmetry is broken by the superpotential on a boundary. Classically, the size $L$ of the fifth dimension is undetermined, with or without supersymmetry breaking, and the effective potential is of no-scale type. The size $L$ is fixed by quantum corrections to the K"ahler potential, the Casimir energy and Fayet-Iliopoulos (FI) terms localized at the boundaries. For an FI scale of order $M_{\mathrm{G}\mathrm{U}\mathrm{T}}$, as in heterotic string compactifications with anomalous $\text{U}1$ symmetries, one obtains $L\sim 1\mathrm{/}{M}_{\mathrm{G}\mathrm{U}\mathrm{T}}$. A small mass is predicted for the scalar fluctuation associated with the fifth dimension, $m_{\rho }\lesssim m_{3\mathrm{/}2}\mathrm{/}(LM)$.