  We study spontaneous supersymmetry breaking in spatially modulated stable or
meta-stable vacua in supersymmetric field theories. Such spatial modulation can
be realized in a higher derivative chiral model for which vacuum energies are
either positive, negative or zero, depending on the model parameters. There
appears a Nambu-Goldstone boson associated with the spontaneously breaking of
the translational and $U(1)$ symmetries without the quadratic kinetic term and
with a quartic derivative term in the modulated direction, and a gapless Higgs
mode. We show that there appears a Goldstino associated with the supersymmetry
breaking at a meta-stable vacuum, where energy is positive, while it becomes a
fermionic ghost in the negative energy vacuum, and zero norm state and
disappears from the physical sector in the zero energy vacuum.

High Energy Physics - Theory;High Energy Physics - Phenomenology