Open string topological amplitudes and gaugino masses

We discuss the moduli-dependent couplings of the higher derivative F-terms (TrW2)h−1, where W is the gauge N=1 chiral superfield. They are determined by the genus zero topological partition function F(0,h), on a world-sheet with h boundaries. By string duality, these terms are also related to heterotic topological amplitudes studied in the past, with the topological twist applied only in the left-moving supersymmetric sector of the internal N=(2,0) superconformal field theory. The holomorphic anomaly of these couplings relates them to terms of the form Πn(TrW2)h−2, where Π's represent chiral projections of non-holomorphic functions of chiral superfields. An important property of these couplings is that they violate R-symmetry for h⩾3. As a result, once supersymmetry is broken by D-term expectation values, (TrW2)2 generates gaugino masses that can be hierarchically smaller than the scalar masses, behaving as m1/2∼m04 in string units. Similarly, ΠTrW2 generates Dirac masses for non-chiral brane fermions, of the same order of magnitude. This mechanism can be used, for instance, to obtain fermion masses at the TeV scale for scalar masses as high as m0∼O(1013)GeV. We present explicit examples in toroidal string compactifications with intersecting D-branes.