Tachyonic decay of unstable Dirichlet branes

We consider an unstable bound system of two supersymmetric Dirichlet branes of different dimensionality (p, p' with p'<p) embedded in a flat noncompactified IIA or IIB type background. We study the decay, via tachyonic condensation, of such unstable bound states leading to a pair of bound D(p-1), Dp'-branes. We show that only when the gauge fields carried by the Dp-brane are localized perpendicular to the tachyon direction, then tachyon condensation will indeed take place. We perform our analysis by combining both the Hamiltonian and the Lagrangian approaches.