  Coset methods are used to construct the action describing the dynamics
associated with the spontaneous breaking of the local Poincare symmetries of D
dimensional space-time due to the embedding of a p-brane with codimension
N=D-p-1. The resulting action is an ISO(1,p+N) invariant form of the
Einstein-Hilbert action, which, in addition to the gravitational vielbein, also
includes N massive gauge fields corresponding to the broken space translation
symmetries which together carry the fundamental representation of the unbroken
SO(N) gauge symmetry and an SO(N) Yang-Mills field localized on the brane. The
long wavelength dynamics of the gravitating p-brane is the same as the action
of an SO(N) vector massive Proca field and a non-Abelian SO(N) Yang-Mills field
all coupled to gravity in d=(1+p) dimensional space-time. The general results
are specialized to determine the effective action for the gravitating vortex
solution in the D=6 Abelian Higgs-Kibble model.
