# Supersymmetry Breaking in Spatially Modulated Vacua

## TL;DR

This paper explores spontaneous supersymmetry breaking in spatially modulated vacua within supersymmetric field theories, revealing unique Goldstone modes and the behavior of the Goldstino across different vacuum energy states.

## Contribution

It introduces a higher derivative chiral model exhibiting various vacuum energies and analyzes the associated spontaneous symmetry breaking and Goldstone modes.

## Key findings

- Presence of a Nambu-Goldstone boson for broken translational and U(1) symmetries.
- Existence of a Goldstino that varies from physical to ghost-like depending on vacuum energy.
- Identification of zero norm states and their disappearance in zero energy vacua.

## Abstract

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.