The paper investigates the properties of chiral operators in N=2 superconformal theories, focusing on the spectral flow of such models under a one-parameter family of twists generated by the U(1) current. It deduces properties of the chiral ring of primary fields and explores conditions under which a superconformal theory can be represented as the fixed point of an N=2 Landau–Ginzburg theory. The paper also examines coset models of Kazama and Suzuki, finding a cohomological characterization of the chiral primary ring and showing how some models can be represented as Landau–Ginzburg models. It discusses the connection between chiral primary states and affine Lie algebra cohomology classes, and shows how the superpotential relates to the cohomological properties of the coset manifold. The paper also explores the spectral flow in N=2 superconformal theories, showing how it interpolates between the NS and R sectors and how it affects the chiral primary states. It discusses the Poincaré polynomial of the conformal theory and its relation to the cohomology of the manifold. The paper concludes that the chiral ring of primary operators is isomorphic to the local ring of the superpotential, and that the Poincaré polynomial of the superconformal theory is the same as that of the corresponding singularity. The paper also shows that the trace of (-1)^F is equal to the multiplicity of the superpotential, and that the conformal dimension of the chiral primary state with the highest charge is related to the singularity index of the superpotential.The paper investigates the properties of chiral operators in N=2 superconformal theories, focusing on the spectral flow of such models under a one-parameter family of twists generated by the U(1) current. It deduces properties of the chiral ring of primary fields and explores conditions under which a superconformal theory can be represented as the fixed point of an N=2 Landau–Ginzburg theory. The paper also examines coset models of Kazama and Suzuki, finding a cohomological characterization of the chiral primary ring and showing how some models can be represented as Landau–Ginzburg models. It discusses the connection between chiral primary states and affine Lie algebra cohomology classes, and shows how the superpotential relates to the cohomological properties of the coset manifold. The paper also explores the spectral flow in N=2 superconformal theories, showing how it interpolates between the NS and R sectors and how it affects the chiral primary states. It discusses the Poincaré polynomial of the conformal theory and its relation to the cohomology of the manifold. The paper concludes that the chiral ring of primary operators is isomorphic to the local ring of the superpotential, and that the Poincaré polynomial of the superconformal theory is the same as that of the corresponding singularity. The paper also shows that the trace of (-1)^F is equal to the multiplicity of the superpotential, and that the conformal dimension of the chiral primary state with the highest charge is related to the singularity index of the superpotential.