Super D-branes revisited

A version of the κ-symmetric super Dp-brane action is presented in which the tension is a dynamical variable, equal to the flux of a p-form world-volume gauge field. The Lagrangian is shown to be invariant under all (super) isometries of the background for appropriate transformations of the world-volume gauge fields, which determine the central charges in the symmetry algebra. We also present the hamiltonian form of the action in a general supergravity background.