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 Kähler potential, the Casimir energy and Fayet-Iliopoulos (FI) terms localized at the boundaries. For an FI scale of order MGUT, as in heterotic string compactifications with anomalous U(1) symmetries, one obtains L∼1/MGUT. A small mass is predicted for the scalar fluctuation associated with the fifth dimension, mρ≲m3/2/(LM).