  It is shown how some field theories in the target-space induce the splitting
of the space-time into a continuous of branes, which can be p-branes or
D-branes depending on what the field theory it is. The basic symmetry
underlying the construction is used to build an invariant action, which is
proved to be off-shell identical to the p-brane (D-brane) action. The coupling
with the abelian ($p+1$)-form in this formulation it is also found. While the
classical brane's embedding couple to the field strenght, the classical fields
couple with its dual (in the Hodge sense), therefore providing an explicit
electric-magnetic duality. Finally, the generic role of the underlying symmetry
in the connection between the target-space theory and the world-volume one, is
completely elucidated.
