Two-loop dilaton tadpole induced by Fayet-Iliopoulos D-terms in compactified heterotic string theories

We calculate the two-loop dilaton tadpole induced by Fayet-Iliopoulos D-terms in heterotic string theories compactified on arbitrary supersymmetry preserving backgrounds. The result turns out to be a total derivative in the moduli and hence receives contribution solely from the boundary of the moduli space. This contribution is shown to be proportional to the square of the coefficient of the one-loop Fayet-Iliopoulos D-term in agreement with what is expected from effective lagrangian considerations