String dynamics, spontaneous breaking of supersymmetry, and dual scalar field theory

The dynamics of a vortex string, which describes the Nambu-Goldstone 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.