Broken sigma-model isometries in very special geometry

Abstract

We show that the isometries of the manifold of scalars in $N=2$ supergravity in $d=5$ space-time dimensions can be broken by the supergravity interactions. The opposite conclusion holds for the dimensionally reduced $d=4$ theories, where the isometries of the scalar manifold are always symmetries of the full theory. These spaces, which form a subclass of the {\em special} K\"ahler manifolds, are relevant for superstring compactifications.