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Complex Linear Effective Theory and Supersymmetry Breaking Vacua

We calculate the low energy effective action of massless and massive complex linear superfields coupled to a massive U(1) vector multiplet. Our calculations include superspace higher derivative corrections and therefore go beyond previous results. Among the superspace higher derivatives we find that terms which lead to a deformation of the auxiliary field potential and may break supersymmetry are also generated. We show that the supersymmetry breaking vacua can only be trusted if there exists a hierarchy between the higher order terms. A renormalization group analysis shows that generically a hierarchy is not generated by the quantum corrections.