Kähler corrections for the volume modulus of flux compactifications

No-scale models arise in many compactifications of string theory and supergravity, the most prominent recent example being type IIB flux compactifications. Focussing on the case where the no-scale field is a single unstabilized volume modulus (radion), we analyse the general form of supergravity loop corrections that affect the no-scale structure of the Kähler potential. These corrections contribute to the 4d scalar potential of the radion in a way that is similar to the Casimir effect. We discuss the interplay of this loop effect with string-theoretic α′ corrections and its possible role in the stabilization of the radion.