Abstract (Elsevier)
It is shown that the extension of the spacetime supersymmetric Green-Schwarz covariant action p -dimensional extended objects ( p -branes) is possible if and only if the on-shell p -dimensional Bose and Fermi degrees of freedom are equal. This is further evidence for world-tube supersymmetry in these models. All the p -branes models are related to superstring actions in d =3, 4, 6 or 10 dimensions by double dimensional reduction (which we generalise to reduction on arbitrary compact spaces), and we also show how they may be considered as topological defects of supergravity theories.