Ghostbusters in higher derivative supersymmetric theories: who is afraid of propagating auxiliary fields?

Understand

We present for the first time a ghost-free higher-derivative chiral model with a propagating auxiliary F-term field (highest component of the chiral multiplet).

• We obtain this model by removing a ghost in a higher derivative chiral model, with Higgsing it in terms of an auxiliary vector superfield.
• Depending on the sign of the quadratic derivative term of the chiral superfield, the model contains two ghost free branches of the parameter regions.
• We find that supersymmetry is spontaneously broken in one branch while it is preserved in the other branch.