A no-go theorem for string warped compactifications

We give necessary conditions for the existence of perturbative heterotic an d common sector type II string warped compactifications preserving four and eight supersymmetries to four spacetime dimensions, respectively. In parti cular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are t hose on Calabi-Yau manifolds with constant dilaton. We obtain similar resul ts for compactifications to six and to two dimensions, (C) 2001 Published b y Elsevier Science B.V.