Abstract
Two supersymmetric versions for the theory of a chiral boson with linearly realized self-duality condition are proposed. In both cases the sector of physical states after canonical quantization contains only modes propagating to the left. The first version describes a chiral boson and its superpartner; the second does not contain nontrivial Fermi degrees of freedom. Both actions are rewritten in a locally supersymmetric form by introducing an interaction with (1, 0) supergravity in the superfield and component forms.
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