  The dynamics of a vortex string, which describes the Nambu-Goldtone modes of
the spontaneous breakdown of the target space D=4, N=1 supersymmetry and
internal $U(1)_R$ symmetry to the world sheet ISO(1,1) symmetry, is constructed
by using the approach of nonlinear realization. The resulting action describing
the low energy oscillations of the string into the covolume (super)space is
found to have an invariant synthesis form of the Akulov-Volkov and Nambu-Goto
actions. Its dual scalar field action is obtained by means of introducing two
vectorial Lagrangian multipliers into the action of the string
