Abstract
We study coset construction of superconformal minimal models using admissible representations of Kac-Moody algebra. In particular, we study supersymmetric minimal models of Wn algebra, and in particular we argue that c = −5/2 cannot be considered as a minimal model of superconformal or super-W3 algebra. In the second part of the paper, we consider superconformal field theories whose perturbations correspond to breather-breather scattering in supersymmetric sine-Gordon equations, and find a family of theories with c = −3N(4N + 3)/2(N + 1), N = 1, 2, 3, …, which is the counterpart of the family of non-unitary theories with c = −2N(6N + 5)/(2N + 3), N = 1, 2, 3, …, among which N = 1 (c = −22/5) is the Yang-Lee edge singularity.
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