Abstract
We discuss spontaneous supersymmetry (SUSY) breaking mechanisms by means of modulated vacua in four-dimensional ${\cal N} =1$ supersymmetric field theories. The SUSY breaking due to spatially modulated vacua is extended to the cases of temporally and lightlike modulated vacua, using a higher-derivative model with a chiral superfield, free from the Ostrogradsky instability and the auxiliary field problem. For all the kinds of modulated vacua, SUSY is spontaneously broken and the fermion in the chiral superfield becomes a Goldstino. We further investigate the stability of the modulated vacua. The vacua are (meta)stable if the vacuum energy density is non-negative. However, the vacua become unstable due to the presence of the ghost Goldstino if the vacuum energy density is negative. Finally, we derive the relation between the presence of the ghost Goldstino and the negative vacuum energy density in the modulated vacua using the SUSY algebra.
Highlights
Understanding the vacuum structure of the quantum field theory under study is the starting point for any analysis
The SUSY breaking due to spatially modulated vacua is extended to the cases of temporally and lightlike modulated vacua, using a higher-derivative model with a chiral superfield, free from the Ostrogradsky instability and the auxiliary field problem
In a recent series of papers, we have studied nontrivial vacua in which the vacuum expectation value (VEV) is not a constant but has a phase that winds along a spatial direction [1,2,3], along a temporal direction [3], or along the direction of the light cone [3]
Summary
Understanding the vacuum structure of the quantum field theory under study is the starting point for any analysis. Because of the fourth-order term being saturated in the nilpotent series of Grassmann numbers, the Grassmannian integral only picks up the bosonic component of the function Λ, and it is straightforward to construct a sixth-order derivative model this way The model constructed this way turns out to be exactly a submodel of the phase-modulated higherderivative scalar field theory models that we constructed in Refs. VI concludes with a summary and a discussion of the open problems
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