  The formation of a confining string (or a p-brane) in a Poincare' invariant
theory breaks spontaneously this symmetry which is thereby realized
non-linearly in the effective action of these extended objects. As a
consequence the form of the action is strongly constrained. A new general
method is described to obtain in a systematic way higher order Lorentz
invariant contributions to this action. We find a simple recipe to promote a
term invariant under the stability subgroup to an expression invariant under
the whole Lorentz group. It is based on the following three steps: in the
saturation of worldsheet (or worldvolume) indices replace the Minkowski metric
with the inverse of the induced metric; in the saturation of indices of the
transverse coordinates describing the position of the extended object replace
the Euclidean metric with a certain new metric; finally replace the field
derivatives of order higher than two with a certain covariant derivative.
Lorentz invariance of the expression modified this way immediately follows. We
find in particular that the leading bulk deviation of the Nambu Goto action in
any space-time dimensions is proportional to the square of scalar curvature.
