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The structure of supersymmetry is analyzed systematically in ${\cal PT}$symmetric quantum mechanical theories. We give a detailed description ofsupersymmetric systems associated with one dimensional ${\cal PT}$ symmetricquantum mechanical theories. We show that there is a richer structure presentin these theories compared to the conventional theories associated withHermitian Hamiltonians. We bring out various properties associated with thesesupersymmetric systems and generalize such quantum mechanical theories tohigher dimensions as well as to the case of one dimensional shape invariantpotentials.

The structure of supersymmetry in ${\cal PT}$ symmetric quantum mechanics