  We present a generalization of the string's Polyakov action that describes a
conformally invariant four dimensional brane. The new extended object is very
different from the traditional D-branes of string theory, but, nevertheless,
shares some structural similarities with the string, especially when it comes
to the low-energy limit of small tension. We introduce a rather rich structure
of tensors that can play a role at low energies. In analogy with the bosonic
string, we initiate the quantization of the new brane discussing the extent in
which it produces a critical dimension of spacetime and Einstein's equations
coupled to a scalar dilaton under some approximations.
