Supersymmetric Semisimple Cardy-Frobenius Algebras

Abstract: Cardy-Frobenius algebra is the algebraic structure on the space of states in open-closed topological field theory. We prove that every semisimple super Cardy-Frobenius algebras is the direct sum of the super Cardy-Frobenius algebras of three simple types. We also apply our results to singularity theory via Landau-Ginzburg models and matrix factorizations.