# Supersymmetry breaking and ghost Goldstino in modulated vacua

## TL;DR

This paper explores spontaneous supersymmetry breaking via spatial, temporal, and lightlike modulated vacua in four-dimensional ${\

## Contribution

It introduces a higher-derivative model that demonstrates SUSY breaking in all modulated vacua types without Ostrogradsky instability, revealing the link between ghost Goldstinos and vacuum energy.

## Key findings

- SUSY is spontaneously broken in all modulated vacua types.
- Ghost Goldstino appears when vacuum energy density is negative.
- Vacua are stable if vacuum energy density is non-negative.

## 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.