D-branes, moduli, and supersymmetry

We study toroidal compactifications of type II string theory with $D$-branes and nontrivial antisymmetric tensor moduli and show that turning on these fields modifies the supersymmetry projections imposed by $D$-branes. These modifications are seen to be necessary for the consistency of $T$ duality. We also show the existence of unusual BPS configurations of branes at angles that are supersymmetric because of conspiracies between moduli fields. Analysis of the problem from the point of view of the effective field theory of massless modes shows that the presence of a two-form background must modify the realization of supersymmetry on the brane. In particular, the appropriate supersymmetry variation of the physical gaugino vanishes in any constant field strength background. These considerations are relevant for the $E_{7\left(7\right)\mathrm{}}$-symmetric counting of states of four-dimensional black holes in type II string theory compactified on $T^6$.