Ghost-free vector superfield actions in supersymmetric higher-derivative theories

We systematically construct ghost-free higher-derivative actions of Abelian vector supermultiplets in four-dimensional ${\cal N}=1$ global supersymmetric theories. After giving a simple example which illustrates that a naive introduction of a higher-derivative term gives rise to a ghost, we discuss possible building blocks for a ghost-free action and explicitly show that their bosonic parts have no ghost mode and the auxiliary field $\boldsymbol{D}$ does not propagate. Higher-derivative terms yield higher powers of the auxiliary field $\boldsymbol{D}$ in the actions, and the D-term equations of motion consequently admit multiple solutions in general. We confirm that the well-known supersymmetric Dirac-Born-Infeld action falls into this class. We further give another example in which the standard quadratic kinetic term (Maxwell term) is corrected by a quartic term of the field strength. We also discuss possible couplings to matter fields and a deformed D-term potential.