D-Brane Dynamics and Logarithmic Superconformal Algebras

We construct the consistent supersymmetric extensions of the operators describing the recoil of a D-brane and show that they realize an N=1 logarithmic superconformal algebra. The corresponding supersymmetric vertex operator is related to the action of a twisted superparticle with twist field determined by the angular momentum of the recoiling D-brane and with explicitly broken kappa-symmetry. We show that the superconformal completion removes the logarithmic modular divergences that are present in the bosonic string loop scattering amplitudes. These features are all consequences of the relationship that exists in these models between worldsheet rescaling and the time evolution of the D-brane in target space.