  Coset methods are used to construct the action describing the dynamics
associated with the spontaneous breaking of the Poincare symmetries of D
dimensional space-time due to the embedding of a p-brane with codimension
N=D-p-1. The resulting world volume action is an ISO(1,p+N) invariant
generalization of the Nambu-Goto action in d=p+1 dimensional space-time.
Analogous results are obtained for an AdS p-brane with codimension N embedded
in D dimensional AdS space, yielding an SO(2,p+N) invariant version of the
Nambu-Goto action in d=p+1 dimensional space-time. Attention is focused on a
supersymmetric extension of the D=6 Minkowski space case with an embedded p=3
brane; a particular realization of which is provided by a non-BPS vortex. Here
both the Nambu-Goto-Akulov-Volkov action and its dual tensor form are
presented.
