On the supersymmetries of branes with fluxes

Abstract: The Dirac-Born-Infled action that describes the dynamics of D branes also allows one to compute the supersymmetries they preserve using the Kappa-symmetry projector. The ''Lagrangian'' expression of this projector depends on the velocity and electric fields of the branes, but not on the corresponding conserved charges. One can also construct the projector in a ''Hamiltonian'' approach, by multiplying the conserved string, brane and momentum charges with the corresponding gamma matrix involutions, adding them to the mass of the brane multiplied by the unit matrix, and normalizing the resulting expression. We show that these two procedures are equivalent.