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PT-Symmetric Non-Hermitian Quantum Field Theories with Supersymmetry

We formulate supersymmetric non-Hermitian quantum field theories with PT symmetry, starting with free chiral boson/fermion models and then including trilinear superpotential interactions. We consider models with both Dirac and Majorana fermions, analyzing them in terms of superfields and at the component level. We also discuss the relation between the equations of motion, the (non-)invariance of the Lagrangian and the (non-)conservation of the supercurrents in the two models. We exhibit a similarity transformation that maps the free-field supersymmetric PT-symmetric Dirac model to a supersymmetric Hermitian theory, but there is, in general, no corresponding similarity transformation for the Majorana model. In this model, we find generically a mass splitting between bosons and fermions, even though its construction is explicitly supersymmetric, offering a novel non-Hermitian mechanism for soft supersymmetry breaking.