  We develop a formalism for computing one-loop gravitational corrections to
the effective action of D-branes. In particular, we study bulk to brane
mediation of supersymmetry breaking in models where supersymmetry is broken at
the tree-level in the closed string sector (bulk) by Scherk-Schwarz boundary
conditions, while it is realized on a collection of D-branes in a linear or
non-linear way. We compute the gravitational corrections to the fermion masses
$m_{1/2}$ (gauginos or goldstino) induced from the exchange of closed strings,
which are non-vanishing for world-sheets with Euler characteristic -1 (``genus
3/2'') due to a string diagram with one handle and one hole. We show that the
corrections have a topological origin and that in general, for a small
gravitino mass, the induced mass behaves as $m_{1/2}\propto g^4 m_{3/2}$, with
$g$ the gauge coupling. In generic orbifold compactifications however, this
leading term vanishes as a consequence of cancellations caused by discrete
symmetries, and the remainder is exponentially suppressed by a factor of
$\exp(-1/\alpha'm^2_{3/2})$.
