Hybrid superstrings on singular Calabi–Yau fourfolds

Two-dimensional hybrid superstring on singular Calabi–Yau manifolds is studied by the field redefinition of the NSR formalism. The compactification on singular Calabi–Yau fourfold is described by N=2 super-Liouville theory and N=2 Landau–Ginzburg models. We examine the world-sheet topological N=4 superconformal algebra, which is useful to identify physical states of the theory. It is shown that the space–time superconformal symmetry is not compatible with this original topological algebra. A new model is proposed by modifying the topological superconformal generators, which is consistent with space–time N=2 superconformal symmetry.