Exactly solvable string compactification on Calabi-Yau manifolds in the Green-Schwarz formalism

We show how the superstring and heterotic string compactification schemes proposed by Gepner using minimal N=2 superconformal field theories may be formulated in the Green-Schwarz formalism. A modular invariant partition function is constructed in this scheme. All the physical states come from the Ramond sector. Two of the four generators of N=1 spacetime supersymmetry transformations are given by the generators of world-sheet supersymmetry, the other two are given by free fermion zero-modes. (orig.)