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

TL;DR

This paper introduces a ghost-free higher-derivative supersymmetric chiral model with a propagating auxiliary F-term, revealing new branches with distinct supersymmetry properties and a conserved U(1) charge related to F-number density.

Contribution

It constructs the first ghost-free higher-derivative chiral model with a dynamical auxiliary F-term, analyzing its ghost-free regions and supersymmetry breaking features.

Findings

Identifies two ghost-free branches depending on derivative term sign.

Shows supersymmetry is spontaneously broken in one branch.

Discovers a conserved U(1) charge associated with the F-number density.

Abstract

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. As a consequence of dynamical F-term field, a conserved U(1) charge corresponding to the number density of $F$ appears, which can be regarded as a generalization of the R-symmetry.