We derive the first complete S-matrices of the supersymmetric sine-Gordon theory for a general value of coupling constant. The spectrum includes not only solitons and antisolitons but also their bound states. The S-matrices are computed based on the soliton S-matrix which was obtained from the S-matrix of perturbed superconformal unitary model. After constructing a superconformal non-unitary model from the coset CFT with admissible representations, we derive the S-matrices of the perturbed superconformal non-unitary model by restricting the SSG S-matrices. We generalize these results to the theories with the fractional supersymmetries.
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It is a pleasure to thank A. LeClair for valuable comments throughout this work, D. Bernard and again A . LeClair for the previous collaboration . Also, we thank P . Argyres, S . Chung, B . Greene, I .G . Koh, C.K. Lee, K . Shigemoto, F. Smirnov, H . Tye and M. Walton for discussions and H.S . Song for his hospitality at the Center for Theoretical Physics in Seoul National University where part of this work has been done . This work was supported in part by the National Science Foundation .