Abstract
The Landau-Ginzburg potentials for the Dn and En modular invariant solutions of the discrete series of the conformal and N=1 superconformal field theories are constructed, in extension of the work of Zamolodchikov on the An solutions. Two relevant primary fields are identified as basic scalar operators and their composites are shown to give the rest of the relevant operators by using the operator product algebra of the conformal field theory. Their composites also give descendants of the two basic fields, and this allows the identifications of the equations of motion and the Landau-Ginzburg potentials. The potentials all resemble the type Dn and En catastrophes.
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