Spacetime scale-invariant super-p-brane actions on enlarged superspaces and the geometry of κ-symmetry

We use the additional variables of suitably enlarged superspaces to write new actions for extended objects, with κ-symmetry, in such a way that the tension emerges from them as an integration constant. Our actions correspond to the spacetime scale-invariant ones previously considered by Bergshoeff et al. once the worldvolume forms introduced there are reinterpreted in terms of fields associated with the coordinates of the enlarged superspaces. It is shown that the κ-symmetry of the new actions is given by a certain type of right local transformations of the extended superspace groups. Further, we also show that the enlarged superspaces that allow for strictly invariant Wess-Zumino terms also lead to strict κ-invariance, i.e., the Lagrangian itself (not only the action) is both supersymmetry- and κ-invariant.