Abstract
The class of two-dimensional scalar supersymmetric models with non-derivative self-interactions is investigated in the context of searching for higher local quantum conservation laws. Using Zimmermann's normal product algorithm in the explicitly supersymmetric formulation, it is shown (at least for weak coupling) that the supersymmetric sine-Gordon model is the only completely integrable model in the above class. The whole infinite set of higher local conserved quantum currents of the latter is constructed. The value β 2 = 4 π of the supersymmetric sine-Gordon coupling constant is shown to be critical in a sense analogous to the case β SG 2 = 8 π in the usual sine-Gordon model.
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